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PHE Landfill Modelling System

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Press and Information

Centre for Radiation, Chemical and Environmental Hazards

Public Health England

Chilton, Didcot, Oxfordshire OX11 0RQ

E: [email protected]

Published February 2014

PHE publications gateway number: 2013353

PHE-CRCE-007

Centre for Radiation, Chemical and Environmental Hazards Public Health England Chilton, Didcot Oxfordshire OX11 0RQ

Approval: October 2013 Publication: February 2014 £21.00 ISBN 978-0-85951-750-8

This report from the PHE Centre for Radiation, Chemical and Environmental Hazards reflects understanding and evaluation of the current scientific evidence as presented and referenced in this document.

PHE Landfill Modelling System

NA Higgins, S Mobbs1, R Kowe2, T Anderson, S Holmes and S Watson

ABSTRACT

The PHE landfill modelling system (LMS) is a linked suite of models developed for the

assessment of doses from the disposal of low level radioactive waste to landfill sites. The

system builds on the experience gained in using the individual models incorporated into the

system, in assessments of landfill sites in the UK. The component models of the system

simulate the key processes in the various media responsible for the transport of radioactivity

from a landfill site to the biosphere and the subsequent doses to humans. This report

describes each of the component models of the LMS and their verification and validation,

discusses their operation together as an integrated system and outlines various options for

further developing and improving the system.

1 Now with EDEN Nuclear and Environment

2 Now with the Nuclear Decommissioning Agency

ii

This work was undertaken under the Environmental Assessment Department’s Quality Management

System, which has been approved by Lloyd's Register Quality Assurance to the Quality Management

Standards ISO 9001:2008 and TickIT Guide Issue 5.5, Certificate No: LRQ 0956546.

Report version 1.0

Changes made to this document since first publication are as follows:

July 2014 Title page – Eden Consulting has been amended to Eden Nuclear and Environment

Table 4 column header has been changed from Kd (m–3

kg–1

) to Kd (m3 kg

–1)

Figure F2 compartment 3 depth label changed from 5 cm to 4 cm

iii

CONTENTS

Abstract i

1 Introduction 1

1.1 Background 1

1.2 Model representation of landfill types 1

1.3 Component models of the PHE LMS 5

2 Verification and Validation of Models 6

2.1 Verification 6

2.2 Validation 6

3 LEACH Model 7

3.1 Description of the LEACH model 8

3.2 Verification and validation of LEACH 8

4 HYDRUS Model 9

4.1 Background 10

4.2 Verification and validation of HYDRUS 11

4.3 Use of HYDRUS as a component of the LMS 13

5 TROUGH Model 13

5.1 Verification and validation of TROUGH 14

5.1.1 Verification with the INTRACOIN study 14

5.1.2 Verification with the PSACOIN level E study 15

6 BIOS and WELL Models 15

6.1 BIOS model 16

6.1.1 Verification and validation of BIOS 16

6.2 WELL model 17

7 Verification and Validation of the Overall LMS 18

7.1 Verification of the LMS 18

7.1.1 Results of the intercomparison of the LMS with the Sniffer study 20

8 Discussion 22

8.1 Future developments 23

9 References 24

APPENDIX A Default Radionuclides 27

APPENDIX B LEACH Model 30

APPENDIX C HYDRUS Model 34

APPENDIX D Comparison of the TROUGH Model with Analytical Results 46

APPENDIX E WELL Model 52

APPENDIX F Comparison of LMS with an Unpublished Assessment 53

INTRODUCTION

1

1 INTRODUCTION

The PHE landfill modelling system (LMS) has been developed to evaluate doses to humans

from a variety of exposure pathways potentially arising from the leaching of radioactive waste

from a landfill site and the subsequent movement of the leachate through the geosphere and

biosphere. The LMS takes the form of a series of linked models that individually represent

generic elements of the loss and migration of radioactivity from a landfill following radioactive

waste disposal and provides a flexible approach to the production of indicative estimates of

the potential radiological consequences arising from the movement of leachate through the

environment. This report describes the component models of the LMS that are used to

represent the movement of leachate through the environment that arise from particular

combinations of design features. The LMS only considers the migration of leachate from

landfill sites; other exposure scenarios which may give rise to radiation doses, such as human

intrusion, are discussed in another report (Chen et al, 2007).

Following an overview of the development of the LMS in Section 1.1 there is a brief discussion

on landfill design in Section 1.2 and an overview of the verification and validation of the

individual models in Section 2. Sections 3 to 7 then describe the main components of the

system in more detail, including a description of the verification and validation of each

component model and the overall system. Finally, Section 8 discusses limitations and

potential future developments of the LMS.

1.1 Background

The full complement of models which constitute the LMS was used for the first time in an

assessment of the radiological consequences of disposing of very low level radioactive waste

by Chen et al (2007). This assessment used the HYDRUS model (Šimůnek et al, 2005), which

can simulate radionuclide transport through the unsaturated zone, for the first time as a

component of the system.

The approach originally taken was to run individual models sequentially and manipulate the

output of one model to generate the input data needed to run the next model in the sequence.

This operation required considerable care, as the outputs and inputs of the component stages

were not compatible without the application of several conversion factors. The LMS now

streamlines the multistage process to produce a convenient tool for assessing the potential

doses from the disposal of waste in landfill sites. The LMS can be run and controlled as a

single entity without the need to adjust manually the input and output data transferred between

component modules. However, to maintain flexibility the option to run the component models

of the LMS separately has also been retained.

1.2 Model representation of landfill types

The EC Landfill Directive (CEC, 1999) classifies a landfill site according to the type of waste

that the site can accept. There are three classes of waste: inert, non-hazardous and

hazardous. The design specifications and operating practices are different for each landfill

class. Figure 1 illustrates schematically the variety of landfill constructions considered by the

LMS. Different combinations of the component models of the LMS are used to represent these

PHE LANDFILL MODELLING SYSTEM

2

different types of landfill. The component models used in the modelling of radionuclide

migration in the different environments are indicated in Figure 1 and discussed in more detail

in Section 1.3. Representative depths for the component regions are shown but these may be

replaced by values characteristic of the particular landfill under study when using the LMS.

FIGURE 1 Generic environments considered by the LMS including the component models used to represent radionuclide transport through and between these environments

From the perspective of undertaking assessments with the LMS model, the principal

differences between the three categories of landfill sites are the barrier requirements designed

to impede the flow of water entering or leaving. Schedule 2 of the Landfill (England and

Wales) Regulations 2002 (Defra, 2002, 2005) and the Framework for Risk Assessment for

Landfill Sites (SEPA, 2002) state that the landfill base and sides shall consist of a mineral

layer that protects the soil, groundwater and surface water. Table 1 sets out the barrier

requirements for the three different types of landfill sites included in the EC Landfill Directive

(CEC, 1999). The mineral layer must be at least equivalent to material with the permeability

and thickness combination given in Table 1. The barrier can be less thick than specified in

Table 1 if the permeability of the barrier is also less and the result is at least as effective as the

combination given in Table 1. The performance of the landfill cap for non-hazardous and

hazardous waste sites is not specified numerically by the Landfill Directive but must meet the

several requirements specified by the regulatory agencies on, for example, a low permeability

layer and surface water drainage (SEPA, 2003).

Radioactive waste is not classified as hazardous waste, but as ‘special waste’, which means

that any of the three types of landfill site can be used. The LMS allows these generic types of

landfill to be easily customised to meet the requirements of a specific assessment.

Within the broad limitations of the component models of the LMS, a wide variety of landfill

designs can be accommodated. Unless an historical site is to be modelled, the design of the

landfill site should be selected to be consistent with the requirements of the Landfill Directive

and current practice, while site- or design-specific information should be incorporated

ground level

clay cap (non-hazardous and hazardous only)

landfill

clay liner

geological barrier (hazardous only)

aquifer

waste

leaching

unsaturated

zone

(geosphere)

saturated

zone

1.5 m

15 m

1 m

5 m

10 m

LEACH

HYDRUS

TROUGHTROUGH

BIOS

INTRODUCTION

3

TABLE 1 Barrier requirements for the three classes of landfill sites included in the EC Landfill Directive (CEC, 1999)

Property Inert Non-hazardous Hazardous

Mineral layer thickness (m)* ≥ 1 ≥ 1 ≥ 5

Mineral layer permeability (m s–1

)* ≤ 1 10–7

≤ 1 10–9

≤ 1 10–9

Cap† Restoration

Top soil cover (m) ≥ 1 ≥ 1

Drainage layer (m) ≥ 0.5 ≥ 0.5

Impermeable mineral layer‡ Yes Yes

Artificial sealing layer No Yes

Gas drainage layer Yes No

* Where the geological barrier does not meet these requirements naturally, it may be reinforced by other means

providing equivalent protection; in any such case, a geological barrier established by artificial means must be at least

0.5 m thick. † Inert landfills may only require a cap for restoration purposes but it should be taken into account if they have

accepted non-inert waste in the past. ‡ As mineral caps must have some residual permeability, the terminology of the Landfill Directive is less precise

for the cap than it is for the liner.

wherever possible. If some of the data required to describe a landfill are unavailable an

assessment can nevertheless proceed, using appropriate generic assumptions. Examples of

the generic landfill designs included in the LMS are shown in Figure 2, where the non-

hazardous and hazardous landfill designs have caps, which inhibit the ingress of rainwater

while functional, whereas the inert landfill type is assumed to have no functionally effective

barrier preventing rain ingress. The assumption was made that the non-hazardous landfill type

has a low-permeability cap, which is assumed to last 50 years, while the cap of the hazardous

landfill type is assumed to last 250 years. These estimates of cap lifetimes and other

representative properties were agreed with relevant organisations as part of a study

sponsored by the Department for Environment, Food and Rural Affairs (Defra) and the

Environment Agency (EA) (Chen et al, 2007).

Landfill designs are required to limit the infiltration of rain and surface water using, for

example, a low permeability cap (SEPA, 2003). The value of the maximum infiltration rate

permitted by the design while the cap is in good repair can be neglected as trivial. Once a cap

is no longer functional, some incident rain passes through the cap and the process of leaching

radioactivity from the waste starts with leachate containing dissolved radionuclides moving

downwards and eventually reaching the top of the clay liner system.

A representative infiltration rate to landfill if no cap is present, or when the cap has fully

degraded, can be derived from an examination of UK rainfall data and representative

estimates of evapotranspiration and runoff. Although in the absence of site- or assessment-

specific information the representative infiltration rate will be uncertain, the LMS assumes that

an infiltration rate of 320 mm y–1

is appropriate (Chen et al, 2007). It should be noted that this

generic infiltration rate is not directly used by the HYDRUS model incorporated within the LMS

(see Sections 4.3 and 7.1 and Appendix C).


4

FIGURE 2 Conceptual designs for the three generic landfill classes. These schematic designs are representative of the variety of sites that might be encountered in the UK (Chen et al, 2007)

The clay liner, which is effectively impermeable for a period specific to each landfill type, slows

down the rate at which leachate reaches the aquifer (the saturated zone). The generic design

of Figure 2 assumes for simplicity that all clay liners are 1 m thick, but they may have different

permeabilities. The lifetime of a compacted clay liner depends on maintaining its low hydraulic

conductivity, which requires the soil/water mixture of the liner to be kept at, or near, complete

saturation (Koerner and Daniel, 1997)*. If the water content is not maintained the

effectiveness of a liner is reduced due to the clay shrinking and cracking. The default

assumption of the LMS is that the clay liner maintains its effectiveness over the timescale of

an assessment.

The hazardous landfill type also has a geological barrier lying under the clay liner. The

geological barrier may be a natural feature or an artificial barrier, made of a low permeability

mineral layer; an additional 5 m clay liner above the aquifer is specified in a previous

assessment (Chen et al, 2007) (see Table 1). The LMS assumes by default that both the clay

liner and any subsequent geological barrier are unsaturated and can be modelled as part of a

single unsaturated zone, where the clay of the geological barrier is assumed to have the same

properties as the clay of the liner†. An alternative perspective, which more naturally

accommodates both the need to maintain the effectiveness of the liner and the unsaturated

zone between the landfill and the aquifer, is to view the landfill as having a geotechnical

membrane over a thin, engineered clay bed which together have an effective permeability

equivalent to a 1 m thickness of engineered clay barrier. This description is likely to bear a

closer resemblance to the actual barrier employed (eg a clay sandwich sealed between

* The water held in the clay is static and tightly bound to the clay particles. † In this context, an unsaturated clay liner is a material with limited mobile water and therefore a low hydraulic

conductivity although as previously noted it has sufficient tightly bound immobile water to maintain its structural

integrity.

Waste

Aquifer

Cap (50 years)

Geological

barrier

Liner

1.5 m

Liner

Non hazardousInert

Waste Waste

Cap (250 years)

Hazardous

Liner

Aquifer

15 m

1 m

5 m

10 mAquifer

Infiltration

Waste

leaching

Unsaturated

zone

Saturated

zone

INTRODUCTION

5

two geotechnical membranes), rather than the 1 m thick clay liner assumed in the generic

design (US EPA, 2001). Leachate migrates through this thin lens zone and into a vadose

zone* of low hydraulic conductivity until eventually reaching the underlying aquifer. Thus, the

LMS assumes that the cap fails after a given period which allows water to enter the landfill,

whereas the landfill liner, which is not assumed to fail catastrophically, allows water in the

landfill to leak continuously into the vadose zone. For simplicity, no modelling distinction is

made between the liner and the remainder of the region between the waste and the aquifer.

However, if information was available and it was thought appropriate the LMS could be used

to model multiple zones with different hydrogeological properties to provide a more complex

analysis of the migration of radionuclides from the waste site to the aquifer (see Sections 4

and 8.1). On reaching the aquifer, the radionuclides in the leachate are transported with

groundwater until released into the biosphere.

1.3 Component models of the PHE LMS

Figure 3 provides a schematic illustration of how the component models of the LMS link

together. A simple leaching model LEACH (see Section 3) provides input to either the

unsaturated zone model HYDRUS (Šimůnek et al, 2005) (see Section 4), or directly to the

aquifer model TROUGH (Gilby and Hopkirk, 1985) (see Section 5). This latter option allows

radioactivity to leach directly from the waste into one or more saturated zones by omitting the

FIGURE 3 Component models of the LMS

* The vadose zone extends from the top of the ground surface to the water table. In fine-grained soils, capillary

action can cause the pores of the soil to be fully saturated above the water table at a pressure less than

atmospheric. In such soils, therefore, the unsaturated zone is the upper section of the vadose zone and not

identical to it. Unless the capillary fringe is specifically discussed, all references in the text to the unsaturated zone

refer to the vadose zone.


6

HYDRUS sub-model of the LMS. This option demonstrates the flexibility of the system, which

can be easily modified to represent landfill designs not included in the Landfill Directive, if

necessary. On reaching the aquifer, the radioactivity is transported until it can discharge into a

river. Doses arising from the potential consumption of plants and animals, are estimated using

the model BIOS (see Section 6.1), while those from ingestion of well water are estimated

using the WELL model (see Section 6.2).

A list of the default radionuclides considered by the LMS is given in Appendix A. This list can

be amended to include additional radionuclides, providing the necessary information can be

supplied for the required component models.

2 VERIFICATION AND VALIDATION OF MODELS

To demonstrate the adequacy of the LMS, a process of verification and validation was carried

out on both the main component models of the LMS (LEACH, HYDRUS, TROUGH, BIOS and

WELL) and the overall system. It was not always possible to apply the validation and

verification methods described in the following sections rigorously. However, the best available

alternatives were used, such as evidence of verification provided by the software developers,

or the validation of parts of a model. Table 2 shows the extent to which verification and

validation were carried out and indicates the sections of this report that provide more details.

2.1 Verification

Verification refers to procedures that show that the mathematical model used is, within

practical limits, a true representation of the conceptual model of the process being emulated

and that the mathematical equations involved are correctly solved. Verification procedures

may vary, depending on the particular characteristics of the model and its end use. Typically,

verification procedures include:

a Reviewing model structure and basic equations by staff other than those involved in

developing the model

b Checking that the model has been correctly implemented

c Comparing computed results with solutions obtained from other models

2.2 Validation

Validation is a technique aimed at demonstrating that a conceptual model, and by implication

the numerical representation derived from it, adequately represents the key processes of

interest in the real environment. The definition of what constitutes an adequate representation

necessarily involves some subjective judgement and may depend on whether the model is

intended for general or site-specific applications and how the model results may be used.

Validation is ideally carried out by comparing model calculations with sets of field observations

and experimental measurements that are independent of the data used to parameterise the

model. In practice, it is not usually possible to validate fully a model representing

environmental transfers of radioactivity because of the lack of sufficient independent data to

LEACH MODEL

7

characterise all the radionuclides, timescales and conditions under which the model is likely to

be applied. However, if full quantitative validation is not possible, partial validation may be

possible or a semi-qualitative approach may be used to check that a conceptual model is likely

to be valid. The latter may use data on the behaviour of chemical analogues derived from

laboratory experiments and be subject to an external peer review of the assumptions used in

developing the model.

TABLE 2 Summary of verification and validation on the PHE LMS

Component Section Verification Validation

LEACH 3.2 By reviewing the model and its

implementation

Direct validation is not feasible over the

relevant timescales, but the underlying model

was qualitatively validated by a literature

search

HYDRUS 4.2 Reported intercomparisons with other

models

Reported comparisons with experimental

results and field data

TROUGH 5.1 By comparison with exact solutions and

other models

No validation

BIOS 6.1.1 Through model intercomparison studies Validation of the full model is not possible

over the long timescales involved. However,

sub-models have been qualitatively validated

and qualitative validation has been carried out

on earlier versions of BIOS

WELL 6.2 By reviewing the model and its

implementation including spreadsheet

calculations

Validation is not possible

Overall system 7 By comparing LMS results with those of

another system

Full validation is not possible but individual

components have been validated as above

The LMS includes version 6B of the BIOS model, referred to as BIOS_6B.

3 LEACH MODEL

The leaching of radioactivity from the waste disposed of in a landfill site once closed is the first

of the sequence of processes represented by the LMS. As indicated in Section 1.2, rainwater

enters the landfill and dissolves a proportion of the waste material. The leachate then moves

downwards through the liner (see Figure 2).

There may be some infiltration during the operational period of the site if the landfill surface is

not adequately covered. The amount of radioactivity lost from the waste due to water

percolating through the site during this period is difficult to calculate because of the variation of

the waste thickness and the unknown amount of infiltration. However, as any effluent

produced during this period is likely to be managed according to current regulations it is

conservatively assumed that no loss of waste occurs during the operational period of the site.

The concentration of activity released from the waste into the leachate is estimated by the

LEACH model, which is discussed briefly in Section 3.1 and in more detail in Appendix B.


8

3.1 Description of the LEACH model

The LEACH model effectively assumes that the disposed radioactive waste is both

homogeneous and distributed uniformly throughout the volume of the landfill, commonly

termed the source zone. This implies that the waste is of uniform thickness and, with the

additional assumption that the waste site is not on a slope, means that the activity released

from the waste is directly determined by the ratio of the infiltration rate of rainwater to the

thickness of the waste through which the water percolates. Strictly, within the confines of a

one-dimensional representation, the waste does not need to be distributed uniformly or to be

homogeneous except in the vertical direction as only the sum of activity in each horizon of the

site is considered. Lack of vertical uniformity could affect the rate of leaching over time

through the effect of a variable water level within the repository as discussed in Appendix B.

However, this is likely to be at least a second-order effect and is therefore not considered

further (see Section 4.3).

The dissolution of the waste is represented by a first-order leaching process that matches the

amount lost at any time with the amount present while accounting for both decay and sorption.

Thus, given a constant infiltration rate, the model of Baes and Sharp (1983) describing the

migration of contaminants through soil is applied in LEACH, as shown in Appendix B.

3.2 Verification and validation of LEACH

The LEACH model implemented within the LMS was verified by staff not involved in its

development through a process of reviewing the governing equations and their software

implementation.

Direct validation of the results from LEACH is not feasible over the timescales relevant to

radionuclide migration in the geosphere. However, it is possible to validate qualitatively the

underlying Baes and Sharp model with other models through a search of the literature. Atomic

Energy of Canada Limited (AECL) and the University of Guelph, Ontario, compared four

models assessing the fate of radionuclides in surface soil including the Baes and Sharp

leaching model (Sheppard et al, 1997). The comparison used a simple soil model in which the

top 15 cm layer is assumed to be instantaneously and homogeneously contaminated.

Subsequent downward migration of the contaminant was modelled until the flow conditions

reached steady state. The AECL model, SCEMR1, was validated against experimental data

and found to behave well numerically. SCEMR1 successfully predicted radionuclide levels

over the short term – less than a single growing season – and the migration of lead in soil

around churches in Denmark over several hundred years (Hawkins et al, 1995). The Baes and

Sharp model was found to compare to within an order of magnitude with SCEMR1. The

SCEMR1 model calculates flow based on the soil moisture budget, with daily atmospheric

input data including root uptake. The simpler Baes and Sharp approach does not calculate

annual water flow or the influence of surface vegetation, but instead uses the net annual

ingress of water as input. The Baes and Sharp model has been implemented in modelling

software such as GENII, used by the US Environmental Protection Agency (Napier et al,

2005) to perform dose and risk assessments of atmospheric releases of radionuclides and

their subsequent deposition.

A validation and verification exercise carried out by McClellan et al (2006) compared

three migration models against field data. The models considered were a compartment

HYDRUS MODEL

9

diffusion model (Landaw and DiStefano, 1984; Kirchner, 1998; Holgye and Maly, 2000), a

convection model (Boone et al, 1985; Bunzl et al, 1994) and the leach rate model included

in the LMS (Baes and Sharp, 1983; McClellan et al, 1991; Abbott and Rood, 1994).

Four experimental sites over which thorium-contaminated sludge was spread and raked into

the top soil in 1961 provided the field data for the intercomparison.

Although the study showed that approximately 75% of the radioactivity was retained in the top

15 cm layer at the four sites, the actual movement of thorium and therefore the effective

migration rates were significantly higher than the calculated migration rates derived for the

compartmental and leach models. However, other factors likely to influence the behaviour of

the contaminants were not considered in the study, such as the physical and chemical

properties of the thorium sludge or the initial preparation of the site.

The compartmental model and the leach rate model yielded broadly consistent results.

However, the migration rate implied by the compartmental model was found to increase with

depth, contrary to observations in the measured soil profile. Other studies using the

compartmental model have observed the same increase in migration rates with soil depth

(Kocher, 1991). McClellan et al (2006) suggest that the assumptions that the diffusion

coefficient is independent of soil depth and the time since deposition occurred might be

unrealistic and a limitation of the compartmental model. In contrast, the migration rates of the

leach model were found to be slightly closer to the measured migration rates, but still lower

and therefore very conservative in terms of the amount of radioactivity assumed to remain in

the upper soil column. The conclusion reached by comparing the three models to measured

field data was to reinforce the importance of using the appropriate physical and chemical

properties governing transport processes of water and solutes in soil. In particular, the

additional site-specific data used by the leach model, in comparison to the other models,

partially compensated for the approximate modelling (see Section 8.1 and the discussion on

BIOS in Appendix F).

If required, the LEACH model may be omitted from the LMS and a more detailed analysis of

infiltration and loss from the waste site made using the HYDRUS model described in

Section 4. However, the added complexity of this would entail is only likely to be justified

under particular circumstances, for example, if it is known that the radioactive waste is not

distributed uniformly throughout the depth of the repository and that puddling of water may

occur to a significant depth. The advantage of including the LEACH model within the LMS is

that it provides a simple approach in a zone likely to be poorly characterised. It also enables

the LMS to be used without the HYDRUS model, if required, as noted in Section 3.1.

4 HYDRUS MODEL

Within the LMS, the term HYDRUS refers to HYDRUS-1D version 3.0, a program for

simulating water flow and the transport of heat or solute in one-dimensional variably saturated

media (Šimůnek et al, 2005)*. The representation of variably saturated media requires more

data and introduces greater modelling complexity to the analysis of waste transport. However,

the greater realism offered by this approach allows more confidence to be placed in the

robustness of the modelling. The problem of defining the partially saturated zone and the

* HYDRUS is also available as a licensed product that can model flow in two and three dimensions.


10

consequences of making different assumptions are discussed in more detail in Appendix C.

However, to provide some context Section 4.1 gives a very brief outline of the behaviour of

water within the unsaturated zone and the problem of solute transport. Section 4.2 discusses

the verification and validation of HYDRUS, while Section 4.3 discusses the use of HYDRUS

for modelling the disposal of radioactive waste to landfill.

4.1 Background

The characteristic measure of a partially saturated soil is the water content defined as the

volume of water per unit volume of the medium. Within a field environment, the potential

energy of soil water has three components: the osmotic, gravity and matric potentials. The first

of these potentials is important in semi-arid countries or if the solute concentration is very high

but can generally be ignored in the UK. The gravitational potential is simply measured by the

height of the water above a chosen reference point, such as the soil surface or the water

table. The final component, the matric potential, has the dominant effect on the transport of

water and dissolved solutes in a partially saturated soil and arises from surface interactions

between soil water and the particles of the medium (Yong, 1999). On a macroscopic scale, the

interaction of water in the interstices of the medium with the surrounding particle matrix

translates into what is termed the matric potential or matric pressure*. In an unsaturated

medium, this pressure is less than atmospheric pressure and therefore normally expressed as

a negative value. The greater the matric pressure achieved, the greater the water content,

with a maximum value of zero representing a fully saturated system. Similarly, a lower, more

negative, pressure implies less water content but the relationship is non-linear and hysteretic

and depends strongly on the pore size distribution of the medium (eg whether it is composed

of clayey or sandy soil). The relationship between the negative head pressure and the water

content is provided by the retention curve. An important related quantity, the hydraulic

conductivity, which determines how easily water moves through a medium, also has a

sensitive and non-linear dependence on the water content. By extension, the transport of

solutes modelled by the LMS and partially dependent on the hydraulic conductivity will have a

sensitive and non-linear dependence on the water content in the unsaturated zone.

Figure 4 illustrates the transient condition of water movement in an unsaturated system

undergoing recharge. The lower zero flux potential (ZFP) in Figure 4 is the boundary region

between water moving to the soil surface to evaporate and moving down to the water table in

the summer, while the upper ZFP represents the advance of the wetting front during the

autumn when infiltration begins to exceed evaporation. On meeting the lower ZFP, the distinct

zones disappear so that during the winter months the soil is at or near complete saturation.

The LMS does not primarily deal with the variation in water content and the movement of

water over seasons or years within an unsaturated zone. However, given an appropriate

dynamic equilibrium representative of the variation in water content with depth, the LMS is

intended to model the transport of solutes within the unsaturated zone. HYDRUS, which is

designed to solve the problem of solutes moving through a partially saturated medium,

provides the LMS with the required capability.

The creators of HYDRUS, who are principally associated with the Department of

Environmental Sciences at the University of California and the US Salinity Laboratory, have

* The matric potential is often measured as a negative head of water or suction pressure.

HYDRUS MODEL

11

provided a review of the development history of the software (Šimůnek et al, 2008). HYDRUS

was chosen for the LMS because of its history of development and ability to model radioactive

decay chains. Within the LMS, HYDRUS is only used to model contaminant transport in the

unsaturated zone (the clay liner and geological barriers, see Figure 2) under conditions of

dynamic equilibrium, although, as noted in Sections 1.2 and 3.2, this scope could be extended

if required. In particular, the LMS does not attempt to determine a suitable equilibrium profile

with depth of the water content in the unsaturated zone between the clay barrier of the waste

site and the receiving aquifer (see Section 8.1 and Appendix C).

FIGURE 4 Combined matric and gravitational potential (after Wellings and Bell, 1982)

The isolation of waste in landfill sites for non-hazardous and hazardous waste is enhanced by

the use of a geological or artificial liner barrier to retard the movement of the contaminant.

HYDRUS is used to model the transport of leachate in this unsaturated barrier between the

areas of outflow from the waste repository and the reception points for that flow at the

receiving aquifer (see Figure 2). The use of HYDRUS to model the retardation of radionuclide

flux from the landfill site can provide a more realistic estimate of the concentration of

radionuclides entering the aquifer than alternative higher estimates that conservatively

assume full saturation. However, the unsaturated zone has a negligible effect on the transport

of radionuclides if it is thin and its saturated hydraulic conductivity is high. When this occurs,

the leachate flux can be assumed to enter the underlying aquifer directly, with the omission of

the retardation effect in the unsaturated zone only introducing a slight increase in the amount

entering the aquifer and the conservatism of the results. A fuller description of the model and

software is available from the HYDRUS user guide (Šimůnek et al, 2005).

4.2 Verification and validation of HYDRUS

An intercomparison between HYDRUS and four other models was carried out by Chen et al

(2002). The other models considered were CHAIN (van Genuchten, 1985), MULTIMED-DP

(Liu et al, 1995), FECTUZ (US EPA, 1989, 1995), and CHAIN 2D (Šimůnek and van Genuchten,

F

l

u

x

Total potential

Dep

th

Gravitational potential

F

l

u

x

F

l

u

x

ZFP wetting soil

ZFP drying soil

Water table

0 -


12

1994) and the intercomparison scenario consisted of a hypothetical release of 99

Tc at the

Las Cruces Trench Site in New Mexico. Sensitivity of three model outputs (peak activity

concentrations, time to peak concentrations at the water table and time to exceed the

maximum critical level at a representative receptor well) to the input parameters were

evaluated and compared among the models for a number of input parameters related to the

soil and chemical properties. In general, the five models provided consistent results in water

flow simulation and predicted very similar breakthrough curves representing the rate of

change in the activity concentration of 99

Tc over time at the receptor point. However, slight

differences were observed in predicted peak concentrations due to the different mathematical

treatments used by the models.

A number of other intercomparisons have been carried out, which have a direct bearing on the

application of HYDRUS within the LMS. For example, Perko and Mallants (2007) compared

the performance of HYDRUS between its one-, two- and three-dimensional forms with the

code PORFLOW. The scenario considered a model representation of a waste container and

assumed a fully saturated system. It was found that there was minimal difference in

representing the loss of radioactivity from the simple geometry of the waste package in using

the one-dimensional HYDRUS model compared to the much more complex three-dimensional

version. The HYDRUS and PORFLOW models displayed similar breakthrough curves with

comparable peak times and fluxes but the different dimensionalities of the model

implementations tended to produce results that were closer to each other than the results of

the other model.

Additional performance measures for HYDRUS were provided by Ardois et al (2007),

who reported both laboratory work by Mazet (2008) and intercomparisons of HYDRUS

predictions with field measurement of water and solute flow of radioactivity released from

Chernobyl waste trenches and material analogues composed of sand columns with a

radioactive tracer.

Dixon (1999) evaluated the effectiveness of HYDRUS-1D and the SHAW model

(Flerchinger and Saxton, 1989) at representing water movement in unsaturated soils in an

area of the radioactive waste management site (RWMS) within the Nevada atomic bomb test

site. Soil-water and atmospheric data collected from a lysimeter site near the RWMS over a

period of approximately five years were used to build the models with initial and boundary

conditions representative of the site. The effectiveness of the HYDRUS and SHAW models in

predicting unsaturated flow in an arid environment was evaluated by comparing measured

storage from the lysimeter with the predicted results from the two calibrated model

simulations. Storage results predicted by the HYDRUS and SHAW models were almost

identical, and agreed reasonably well with actual lysimeter storage and measured moisture

profiles. However, the models were sensitive to the large seasonal fluctuations in

meteorological parameters.

In addition, the HYDRUS user manual (Šimůnek et al, 2005) provides further examples of the

verification and validation of the model, which are summarised in Appendix C and provide an

indication of the scope of the model. However, these additional tests and comparisons are not

relevant to the modelling tasks required of HYDRUS within the LMS. Thus, although they

confirm the scope and quality of the model in many areas they can only provide background

reassurance that the model is robust and likely to provide reasonable results when applied in

the context of the LMS.

TROUGH MODEL

13

4.3 Use of HYDRUS as a component of the LMS

The intercomparisons discussed in the previous section and Appendix C illustrate that the

HYDRUS model has been applied to the modelling of the migration of radioactive waste from

disposal sites or characterising water movement through such sites and has performed well

when subject to validation and verification trials. However, it should be remembered that the

model is designed for assessments for a particular location specified by the detailed input data

required and a particular period during which model parameters either have a known time

dependence or can be assumed to be constant. In addition, the HYDRUS user interface only

supports input and output times measured in days at its lowest resolution, which is not ideal

when considering waste migration from disposal sites over hundreds or thousands of years.

HYDRUS can also be applied to the entire process of leaching and migration from a landfill

to an aquifer through an unsaturated zone with eventual abstraction of contaminated drinking

water at a well, as shown by Merk (2010). Merk assumed that the leaching of radioactivity

from low activity rubble added to a waste site and its migration through a liner and into an

unsaturated zone can be modelled by HYDRUS and that a second HYDRUS run can be

used to model the lateral flow of the contaminant entering the receiving aquifer. However,

although the paper illustrates the potential of this approach only trial parameters were applied

in the analysis.

Although HYDRUS generally provides indicative results when used within the LMS, it allows

the exploration of potential effects on radionuclide migration of including transport in an

unsaturated zone and using different saturation states without precluding more quantitative

analysis. For example, HYDRUS could be used to find a matric potential and moisture

distribution representative of the unsaturated zone over the long periods of interest in

radioactive waste management, which could in turn be applied within other components of the

LMS. This additional option is potentially computationally much more intensive than assuming

a known saturation state and is discussed in more detail in Appendix C (see also Section 8.1).

5 TROUGH MODEL

The groundwater transport model TROUGH (transport of radionuclide outflows in under-

ground hydrology), originally developed by Polydynamics Ltd in the 1980s (Gilby and Hopkirk,

1985), is a one- or two-dimensional transport model that describes the movement of

radionuclides and their progeny in multiple geological layers. The model assumes a known

steady-state flow rate in each stratum and incorporates geochemical features such as

solubility limitation and the effect of equilibrium and non-equilibrium sorption of radionuclides

on to solid surfaces in porous media. The one-dimensional version of TROUGH is used within

the LMS to model the movement of contaminants in an aquifer (the saturated zone of

Figures 1 and 2). The radionuclides entering the saturated zone described by TROUGH are

subject to advection, dispersion and sorption as they travel through the geosphere. The model

can also represent fracture flow using matrix diffusion in an equivalent porous continuum. The

assumption implicit in the use of TROUGH is that any changes in groundwater flow conditions

during the modelling period can be neglected. This assumption is appropriate for long-term

far-field assessments; however, if the transient behaviour of groundwater flow is likely to be


14

important more detailed modelling would be required. The TROUGH model is described in

detail in the TROUGH user guide (Gilby and Hopkirk, 1985).

5.1 Verification and validation of TROUGH

Several verifications of the TROUGH model are discussed in the following sub-sections.

Despite a literature search of papers from the validation of geosphere flow and transport

models exercise (GEOVAL) (NEA/SKI, 1991, 1995), no evidence of the direct validation of

TROUGH was located. Indirect validation can be inferred to some extent from the limited

validation of other models that share the same theoretical foundations (OECD/NEA, 1997).

5.1.1 Verification with the INTRACOIN study

The original version of TROUGH was verified in the international nuclide transport code

intercomparison (INTRACOIN) Study (Swedish Nuclear Power Inspectorate, 1984, 1986). The

INTRACOIN study was divided into three levels:

a Level 1 compared the results of several numerical codes for seven different test cases

and, if possible, compared the results to analytical solutions of the transport equations

b Level 2 was principally concerned with the ability of the various computer codes to

simulate field experiments involving radioactive tracers

c Level 3 was a limited sensitivity analysis to determine the effects of including or

excluding various transport phenomena, such as dispersion, sorption and matrix

diffusion, on the results obtained from the various codes

Three of the seven test cases included in level 1 of the INTRACOIN study were amenable to

modelling with TROUGH and produced results in good agreement with those of the other

codes in the study.

The cases considered in level 2 of INTRACOIN were divided into those dealing with porous

media and those dealing with fractured media. The two-dimensional version of the TROUGH

code was used for one of the porous media cases. The fractured media cases were not

considered by either the one- or two-dimensional version of TROUGH.

The one-dimensional version of TROUGH was used in the level 3 INTRACOIN study to

investigate the effect of including different processes in the transport calculation. A central

case and 11 variations were considered by five teams using different models. The results from

the different models generally differed by less than 10% and demonstrated that the diffusion of

radionuclides into the rock matrix was the most important retardation mechanism for the

particular scenario analysed.

These studies demonstrated that the TROUGH model provides a representation of the

important physical processes associated with the modelling of transport in saturated porous

media that is consistent with the results of other models.

BIOS AND WELL MODELS

15

5.1.2 Verification with the PSACOIN level E study

A further verification of the one-dimensional version of TROUGH was made by comparing

TROUGH as used within the LMS with results of the second NEA probabilistic system

assessment code intercomparison exercise (PSACOIN) (OECD/NEA, 1989), known as level E

because it provides an exact solution. The existence of an exact solution provided a

benchmark against which all the codes participating in PSACOIN could be compared.

Although the TROUGH model was included in the original PSACOIN exercise, it was

considered appropriate to verify that in the process of modifying the pre-processor of

TROUGH to adapt it for use as part of the LMS no substantial changes had occurred.

Therefore, TROUGH, with the revised pre-processor used in the LMS, was retested against

the PSACOIN level E study and the results of the comparison results are reported in detail in

Appendix D. The level E specification of a deep geological disposal facility was necessarily

limited by the requirement to be amenable to an analytical solution (Robinson and

Hodgkinson, 1987). Thus, the repository was represented very simply without any

complexities of physical structure or chemical composition. After a delay representing failure

of the primary containment, the release of radionuclides to the geosphere depends only on the

leach rate and the inventory, modified by radioactive decay. The released radionuclides were

then transported by groundwater through two geosphere layers with different hydrogeological

properties. The radionuclides leaving the geosphere were assumed to enter a simple

biosphere – a dilution model of drinking water – from which doses were estimated.

Four radionuclides were considered for each of the three test cases of the PSACOIN level E

study: 129

I and 237

Np with its progeny 233

U and 229

Th. The source term was always assumed to

leach at a constant rate following the failure of the initial containment. The quantities

compared with the exact solutions were the peak flux and the time of occurrence at the end of

the first layer and the peak dose at peak time from ingestion of drinking water abstracted from

a river at the end of the second layer

The maximum discrepancy between the LMS results from TROUGH and the exact solution for

any of the radionuclides and test cases was found to be 1.4% for the flux at the end of the first

layer and 3.2% for the peak dose.

Appendix D also compares the flux calculated using TROUGH to the results of the analytical

model CHAIN (van Genuchten, 1985) for 129

I and 239

Pu and some of its progeny. In the case of 129

I a further comparison was performed between the flux calculated by TROUGH in two-layer

mode and those obtained by running TROUGH sequentially as two consecutive single layers.

This intercomparison showed that the results produced by TROUGH are in good agreement

with those obtained using an independent analytical model.

6 BIOS AND WELL MODELS

Two exposure pathways are normally considered for the radionuclides released into the

biosphere following their transport from the waste site by groundwater. The first is the

consumption of the groundwater extracted directly by a well sunk into the transporting aquifer.

The second is the consumption of food that is either irrigated with water abstracted from a

river or lake receiving groundwater, fish from the river or lake, or food grown or reared on soil

that takes up groundwater released from an underlying aquifer. In the LMS doses from the


16

consumption of food are modelled using the compartmental model BIOS, which simulates the

movement of radioactivity through the biosphere, while doses from the ingestion of drinking

water abstracted from the transporting aquifer, are estimated using the simple model WELL.

BIOS also provides estimates of the possible dose from drinking contaminated water.

However, the WELL model provides a higher estimate than BIOS by modelling the direct

abstraction of water from the aquifer, before any dilution with uncontaminated water in the

river or lake receiving the aquifer discharge occurs.

6.1 BIOS model

The BIOS model divides the terrestrial and aquatic biosphere into a number of idealised

compartments. BIOS assumes that the contents of any compartment are instantaneously well

mixed and that the rate of transfer between compartments can be approximated using

equilibrium rate constants representative of the different processes operating between the

compartments. The conceptual model can be represented by a set of linear first-order

differential equations with constant coefficients governing the rate of movement of

radionuclides between compartments and can be solved using standard numerical methods.

This model is simpler than the approach employed by HYDRUS (see Section 4) with no

consideration given to variations in the water content of the soil and the transport of

radioactivity in an unsaturated zone subject to the varying effects of rainfall and

evapotranspiration from the covering vegetation. The use of a simpler model, such as BIOS,

reflects the greater uncertainty in the competing processes involved at future times, more

distant locations and greater spatial extents affected by the discharging aquifer. The BIOS

model is also considerably broader in scope than HYDRUS, providing dose estimates for

intakes of a wide range of foods as well as from inhalation and external exposure. The

idealised compartments of the BIOS model represent elements of the environment such as

soil layers or parts of plants and animals that enable estimates to be made of the activity

concentrations in each compartment as a function of time. Particular combinations of

compartments are often described as models for particular foods or environmental materials

and Appendix F describes briefly the models used to represent the transfer of radioactivity

between soil, plant and animal for some of the foods considered by BIOS.

6.1.1 Verification and validation of BIOS

The version of BIOS implemented in the LMS is BIOS_6B. Each version of BIOS was

benchmarked against previous versions to ensure that improvements to particular parts of the

model did not adversely affect other parts. Different versions of BIOS have been validated

through model-model intercomparison studies: BIOS_3A (Martin et al, 1991) through

the biosphere model validation study (BIOMOVS) (SSI, 1993), and BIOS_5C through the

biosphere models for safety assessment of radioactive waste disposal (BIOMOSA) study

(Pröehl et al, 2005). BIOS_3A was also subjected to detailed peer review as a result of its use

in the Nirex research programme (Baker et al, 1995). A simplified version of BIOS, called

MiniBIOS, was verified by means of detailed benchmarking against BIOS_3A for the

PACOMA study (CEC, 1991) and through model-model comparisons within an NEA

probabilistic system assessment code (PSAC) user group and BIOMOVS II (SSI, 1996).

BIOS AND WELL MODELS

17

It is not possible to validate BIOS quantitatively because of the long-term nature of the

predictions for which it is most commonly used. In addition, available data have often been

used to parameterise the component models. However, most of the component models of

BIOS and MiniBIOS are based on models that have been qualitatively validated to some

extent, even if only for a few radionuclides and for short-term predictions.

The validations of BIOS_3A and MiniBIOS carried out within the BIOMOVS programmes were

qualitative. BIOMOVS was an international cooperative study to test models designed to

quantify the transfer and bioaccumulation of radionuclides and other trace substances in the

environment using measurements of radioactive fallout from the Chernobyl nuclear plant

accident in 1986. The first phase of BIOMOVS (BIOMOVS I) was completed in 1990 (SSI,

1993) while the second phase, BIOMOVS II, ran from 1991 to 1996 (SSI, 1996). Similarly, the

IAEA programme on the validation of model predictions (VAMP) (IAEA and CEC, 1993) was

followed in 1996 by the IAEA programme on biosphere modelling and assessment

(BIOMASS) (Linsley and Torres, 2004). The BIOMASS programme followed the same

approaches used in VAMP and BIOMOVS for the testing of models and continued the work

started in BIOMOVS II to define a reference biosphere for use in assessments of the long-

term safety of underground radioactive waste repositories. BIOS_3A was not considered in

the BIOMASS programme, which ended in 2001. However, there then followed the biosphere

models for safety assessment of radioactive waste disposal (BIOMOSA) study (Pröehl et al,

2005) which used the reference biosphere methodology specified within BIOMASS to develop

a generic biosphere tool based on BIOS_5C, to compare five site-specific biosphere models

for five typical locations in Europe. In general, there was an acceptable agreement between

the results of the generic biosphere tool, for both the deterministic and stochastic calculations,

with the results from the site-specific models.

In addition to the intercomparison studies discussed above, and to demonstrate the

consistency of BIOS results over time and developing technology, Appendix F compares

results obtained with earlier versions of BIOS with those from the version used within the LMS

(BIOS_6B).

6.2 WELL model

Well water may be used to irrigate crops or to provide drinking water for livestock. However,

these exposure pathways are usually radiologically less important than the use of well water

for human consumption and are not considered by the simple well water model, WELL,

included in the LMS. The model is described in detail in Appendix E but, essentially, it applies

a correction factor to the activity concentration predicted at the sampling location in the aquifer

by TROUGH to account for the filtering of the water to remove suspended sediment and then

calculates the dose to individuals consuming the filtered water.

The results of the WELL model used in the LMS can be reproduced by a spreadsheet

calculation that implements the essential elements of the methodology discussed in Appendix E.

However, the spreadsheet calculation only verifies that the equations are correctly

implemented in the LMS; a lack of suitable information prevented validation of the model.


18

7 VERIFICATION AND VALIDATION OF THE OVERALL LMS

The previous sections have illustrated the verification and validation of the individual models

contributing to the LMS. This section details the verification of the system as a whole by

comparing the results of LMS calculations using different combinations of these models with

each other and with an independent landfill assessment. A comparison with earlier assessments

using an alternative geosphere model (GEOS) is also reported in Appendix F. A full quantitative

validation of the overall system is not possible due to the long timescales involved.

7.1 Verification of the LMS

The verification exercise undertaken was divided in two parts: a comparison between two

different combinations of the component models of the LMS and a comparison with the results

of the case study for the Sniffer consortium undertaken by Galson Ltd (Reedha and Wilmot,

2005), hereafter referred to as the Sniffer study. The two LMS model combinations that were

compared use, respectively, the component models LEACH, TROUGH and WELL or LEACH,

HYDRUS, TROUGH and WELL. For convenience, these combinations are referred to as the

TROUGH (T) and HYDRUS and TROUGH (HT) options, respectively. The first option (T)

assumes that there is a fully saturated zone below the landfill. For this option the radionuclides

leached from the landfill site enters a two layer saturated region of barrier and aquifer

modelled by TROUGH. In the second option (HT) the barrier is modelled by HYDRUS and the

aquifer by TROUGH. This option allows a range of saturation states to be represented,

including fully saturated, for the zone between the landfill and the aquifer. The HT option was

evaluated under both saturated and unsaturated conditions to give three sets of results

together with an independent set of results for the same scenario*.

The model used in the Sniffer study implements a framework developed by the Environment

Agency (EA) to assess sites for special precaution burial disposals with input data derived for

a generic landfill site subject to a particular migration scenario. The model assumes a fully

saturated zone below the landfill site. The generic landfill site described in the EA framework

and the associated data were used in the intercomparison between the LMS and the Sniffer

study. The parameter values in each LMS combination were either set to their default value or

to a value from the scenario adopted in the Sniffer study (Reedha and Wilmot, 2005). The

parameters of the landfill site are given in Table 3, while Kd values of the radionuclides

considered in the intercomparison are shown in Table 4. The outputs calculated for the

intercomparison exercise were the peak annual effective doses from the consumption of well

water by a person representative of a group of people with very high intake rates of drinking

water arising from the disposal of 1 MBq of activity for each radionuclide and the time the peak

effective dose occurs for each of the disposed radionuclides. The peak times were not

presented in the report of the Sniffer study.

* The only difference between saturated and unsaturated when applied to the use of HDRUS in this context is that

the former assumes a matric pressure of zero.

VERIFICATION AND VALIDATION OF THE OVERALL LMS

19

TABLE 3 Parameter values of the landfill site adopted in the Sniffer model (Reedha and Wilmot, 2005)

Parameter Value

Surface area (m2) 42.39 10

4

Volume (m3) 4.0 10

6

Distance to water abstraction point (m) 2.5 102

Drinking water consumption rate (m3 y

–1) 7.3 10

–1

Net water infiltration rate after cap failure (m y–1

) 1.55 10–1

Time of cap failure (y) 1.0 102

Thickness of effective geological barrier (m) 1.0 100

Thickness of unsaturated zone (m) 2.0 100

Total barrier thickness for modelling as a single zone (m) 3.0 100

Hydraulic conductivity of barrier (m s–1

) 1.0 10–9

Bulk density of barrier (kg m–3

) 2.0 103

Porosity of barrier 5.0 10–1

Thickness of groundwater zone (m) 3.0 101

Hydraulic gradient 5.0 10–2

Hydraulic conductivity of groundwater bearing rock (m s–1

) 1.0 10–5

Bulk density of groundwater bearing rock (kg m–3

) 2.3 103

Porosity 4.0 10–1

TABLE 4 Kd and decay constants of the radionuclides considered in the intercomparison between the LMS and the Sniffer model (Reedha and Wilmot, 2005)

Radionuclide Kd (m3

kg–1

)

Parent Progeny Waste Barrier Aquifer Decay constant (y–1

)

3H 0.0 0.0 1.0 10

–6 5.63 10

–2

14C 0.0 1.0 10

–3 1.0 10

–6 1.21 10

–4

36Cl 0.0 1.5 10

–2 1.0 10

–6 2.30 10

–6

99Tc 0.0 1.0 10

–3 1.9 10

–1 3.25 10

–6

129I 0.0 1.0 10

–3 1.0 10

–6 4.41 10

–8

232Th 0.0 6.0 5.0 10

–1 4.95 10

–11

228

Ra 0.0 9.0 1.0 10–3

1.21 10–1

228

Th 0.0 6.0 5.0 10–1

3.63 10–1

238U 0.0 4.6 10

–2 1.0 10

–2 1.55 10

–10

234

U 0.0 4.6 10–2

1.0 10–2

2.84 10–6

230

Th 0.0 6.0 5.0 10–1

9.00 10–6

239Pu 0.0 7.6 1.0 10

–1 2.88 10

–5

235

U 0.0 4.6 10–2 1.0 10

–2 9.84 10

–10

Only the parent radionuclides were assumed to be present initially in the waste disposed of.


20

7.1.1 Results of the intercomparison of the LMS with the Sniffer study

The results of the intercomparison between the LMS and the Sniffer study are shown in

Table 5. The table reports results for three variants of the LMS: option T, option HT with a fully

saturated barrier (matric suction of 0 m) and HT with the default matric suction assumed by

Chen et al (2007) of –1 m. The results presented in Table 5 show that for many radionuclides

there is broad agreement between the peak dose estimated by the LMS for both the T and HT

options under fully saturated conditions. The largest difference is for 3H for which the peak

dose calculated by the LMS under saturated conditions for option T differs from the peak dose

calculated for option HT by a factor of 10. This difference in the estimated dose is consistent

with the difference in the estimated time of the peak dose and peak flux of the breakthrough

curve predicted by the T or HT options, as shown in Figure 5.

As noted in Section 4.3, the use of HYDRUS within the LMS enables the system to take

account of the effect of transporting radionuclides through partially saturated soils. It is

important to note that one consequence of the implementation of HYDRUS within the LMS is

that calculations with a fully saturated barrier for options T and HT are not equivalent and

therefore the results cannot be expected to agree. The calculation for option HT does not

consider the effect of water puddling within the waste site and does not require the Darcy flux*

below the liner to match the average rate of rainwater ingress. This difference does not affect

the doses for longer-lived radionuclides, estimated under saturated conditions by the LMS,

which are in good agreement when calculated using the T and HT options. Figure 5 and

Table 5 demonstrate that the two options available in the LMS to describe radionuclide

transport under saturated conditions produce broadly similar doses, provided the half-lives of

the radionuclides are long in comparison to the travel times considered (see also Section C5).

Figure 5 demonstrates that the most important difference between the results for options T

and HT under saturated conditions is a delay in the peak time due to the difference in water

velocity assumed by the two approaches. The results of Table 5 contrasting the HT option

applied under fully and partially saturated conditions demonstrates the effect that the reduced

water content of partial saturation may have on the expected doses. In addition, the water

velocity effect observed between the T and HT options under saturated conditions shown in

Figure 5 will also apply under partially saturated conditions and lead to an underestimate of

the flux as the effect of partial saturation on the hydraulic conductivity is overestimated. As

discussed in Section 4.1, the matric potential and saturation state of the soil are likely to vary

with depth and interact in a complex way with the head of water expected in the landfill.

The peak dose for 239

Pu calculated by any of the LMS options considered differs markedly

from the much larger peak doses calculated in the Sniffer study. This result may reflect the

cautious nature of the Sniffer calculations but no specific information is supplied by the case

study that would indicate a difference in the treatment of 239

Pu migration via groundwater in

comparison to other radionuclides (see Section D2). The reverse effect occurs for 232

Th when

the calculation by the LMS is compared with the Sniffer result. The migration of 232

Th is

difficult to model due to the very long breakthrough time and this difficulty may be exacerbated

in the simple Sniffer approach and lead to the less conservative Sniffer result. However, as no

information on the timing of the peak dose is reported in the Sniffer study a definitive

conclusion cannot be drawn.

* The Darcy flux or specific discharge is the average flux crossing a surface large enough to be viewed as a

homogeneous material with a given porosity. It must match the net rainfall infiltration rate entering the volume if

there is no swelling or shrinkage of the medium (see Appendix B).

VERIFICATION AND VALIDATION OF THE OVERALL LMS

21

FIGURE 5 3H breakthrough curve for the Sniffer scenario calculated under saturated conditions

using the LMS options T or HT. The broken line represents the results for option T delayed by 35 years, the approximate difference in the peak times between the two options

TABLE 5 Results of intercomparison between the Sniffer study and the LMS

Radionuclide

LMS excluding HYDRUS (option T)

LMS including HYDRUS (option HT)

Sniffer case study Fully saturated barrier Unsaturated barrier

Peak dose (Sv y

–1)

Peak time (y)

Peak dose (Sv y

–1)

Peak time (y)

Peak dose (Sv y

–1)

Peak time (y)

Peak dose (Sv y

–1)

3H 2.3 10

–15 1.18 10

2 2.4 10

–16 1.53 10

2 1.5 10

–20 2.14 10

2 2.8 10

–14

14C 3.5 10

–11 1.64 10

2 2.1 10

–11 3.51 10

2 3.0 10

–13 2.33 10

3 2.6 10

–11

36Cl 8.1 10

–12 5.93 10

2 3.3 10

–12 2.82 10

3 6.5 10

–19 3.33 10

3 6.6 10

–12

99Tc 6.4 10

–13 4.51 10

3 4.8 10

–13 5.45 10

3 2.6 10

–13 9.97 10

3 4.4 10

–14

129I 6.9 10

–9 1.64 10

2 4.2 10

–9 3.52 10

2 7.7 10

–11 2.66 10

3 3.2 10

–9

232Th 6.5 10

–9 1.87 10

5 5.4 10

–9 1.07 10

6 7.9 10

–11 1.17 10

7 3.0 10

–17

238U 1.3 10

–10 1.81 10

3 5.6 10

–11 8.64 10

3 1.0 10

–12 9.28 10

4 3.0 10

–11

239Pu 2.1 10

–16 4.31 10

3 1.9 10

–16 1.12 10

4 2.6 10

–17 1.36 10

5 1.8 10

–13

The effect of partial saturation on the results is strongly influenced by the time required with

respect to the half-life of the radionuclide to pass from the low saturation regime into the

aquifer. Highly mobile long-lived radionuclides are least affected by partial saturation, while

short-lived less mobile radionuclides may decay completely before they can cross a partially

saturated zone. In distinction to the Sniffer model, the LMS version that includes HYDRUS

allows the potential effect of an unsaturated zone between the waste and the aquifer to

be considered.


22

8 DISCUSSION

The LMS estimates the amount of radioactive waste material leaching from a landfill site,

models the subsequent movement of the released solutes through the geosphere and

biosphere, and calculates the resulting doses to humans from the associated exposure

pathways. This system is applicable to landfill sites that operate in Europe and is designed to

support simple assessments and to provide indicative results through the simple

representation of key processes. A simple one-dimensional model of a landfill requires the net

flow of water entering the landfill to match the amount of water assumed to enter the aquifer

from the waste site. However, the LMS, when used with HYDRUS, is not yet designed to

conserve automatically the net amount of water traversing the system and transporting the

radioactivity held in the waste site to the aquifer. The LMS in this configuration therefore tends

to overestimate the time of peak breakthrough and due to radioactive decay and dispersion

potentially underestimate the peak and total amount of activity reaching the aquifer.

The verification and validation of the component models described in this report demonstrate

the robustness of the individual components of the LMS. A partial verification of the entire

system was undertaken through the comparison of the LMS with the Sniffer model. A more

detailed intercomparison, with Sniffer and if possible other models, would provide additional

insights into the capabilities and limitations of the LMS and the robustness of the results

it produces.

A novel feature of the LMS is the ability to use HYDRUS to model the unsaturated zone

between the radioactive waste and the aquifer. The use of HYDRUS within the LMS provides

an indication of the potential significance of an unsaturated zone on the timing and magnitude

of doses. However, the disadvantage of using HYDRUS within the LMS is that the results

produced are likely to underestimate the potential doses because of the way HYDRUS has

been incorporated into the LMS. Fortunately, the LMS allows a conservative (dose

maximising) calculation to be undertaken that omits the use of HYDRUS and in most

circumstances results in estimated doses well below regulatory concern. It is therefore only for

a limited number of scenarios when an alternative implementation of the HYDRUS model

within the LMS, producing a smaller and more realistic overestimate, is required to provide

additional reassurance on the low level of predicted doses. The resolution of this problem

would allow the LMS to provide more realistic estimates of releases to the biosphere when

HYDRUS is included, rather than indicative results. Potential solutions to this problem are

considered in Section 8.1.

The LMS is a flexible combination of models that can be used in many ways. However, great

care should be exercised when setting up a calculation, as the input files for one model often

require that the information supplied by other models is reformulated. The LMS does not

check that repeated data are used consistently or even that the same number of progeny are

used by different models.

In summary, the LMS can be used for quantitative but cautious assessments by omitting the

HYDRUS option. It is recommended that the LEACH option to allow direct input to TROUGH

by bypassing HYDRUS is also omitted as LEACH was designed to supply the leachate flux

from the parent in the landfill to HYDRUS while omitting any contribution from ingrown

progeny. The TROUGH program has a built in pre-processor program that provides more

functionality than available with LEACH such as a leachate flux for the ingrown progeny.

DISCUSSION

23

Therefore, for the purposes of the type of assessment likely to be carried out by PHE the

default mode of the LMS is to include only the TROUGH, BIOS and WELL models, while the

other components (LEACH and HYDRUS) are used only for research and development.

8.1 Future developments

A number of improvements could be made to the design of the LMS as outlined below. For

example, it would be useful to identify the characteristic parameter combinations when

saturation is not expected to occur. If a less cautious and more realistic calculation is required

under such circumstances then generic pressure profiles could be developed that would

complement the generic waste site designs and parameterisation and allow HYDRUS as

currently implemented to be used in a semi-quantitative way. The development of such a

profile would allow, as far as possible, the net infiltration of rainfall assumed for the waste site

and the flow into the aquifer to match and thus provide a consistent steady-state

representation*. This approach would enable semi-quantitative results to be produced within

the existing framework (Kao et al, 2001). As discussed in Appendix C data are available on

the hydrological parameters of the soils near landfill sites throughout the UK.

In a further refinement, HYDRUS may be run in an iterative mode to determine the equilibrium

water flow, matric potential and hydraulic conductivity. This option can be computationally

expensive but may be required under certain circumstances to achieve a dynamic water

balance. The approach should allow more realistic results to be produced than those obtained

by omitting the unsaturated zone, while remaining cautious when calculating doses. Changes

in the way HYDRUS is run would allow bathtubbing events, when leachate from the waste site

overflows, to be linked to particular rain sequences either when particular scenarios are

investigated or as part of an uncertainty analysis.

The capabilities provided by HYDRUS can also be used to review and refine the assumptions

surrounding the way radioactivity initially enters and then moves through the biosphere from

the transporting aquifer. The soil included in BIOS is assumed to be fully saturated and

therefore does not consider the modelling features for unsaturated soil included in the

HYDRUS model; however, the advection–diffusion modelling of HYDRUS together with the

information on soils in the UK (see Appendix C, Section C2.1) can improve the representation

and calibration of the BIOS soil model.

A number of assumptions made in the current version of BIOS that stem from earlier versions

of the model (Martin et al, 1991), such as those used to calculate doses arising from releases

of 3H and

14C into the biosphere via an aquifer, would benefit from a review.

Consideration could be given to linking the component models in a more seamless and

effective way, which would have the advantage of removing some of the limitations of the

current system. For example, in some circumstances it would be advantageous to start the

LMS with HYDRUS rather than the LEACH model. The HYDRUS model can cope with a

larger number of input and output fluxes as well as sources within the modelled volume so that

HYDRUS, in addition to modelling the unsaturated zone below the waste site, could be

applied to the variably saturated zone above the waste liner. This more comprehensive

* It may be difficult to achieve an exact match when the water flow solution is applied in the LMS if alternative

software, grid sizes or even boundary conditions are used to solve the water flow problem from those used to

solve the solute transport problem using HYDRUS.


24

approach to the representation of a waste site would remove many of the limitations of the

current system. However, such complexity will not always be required and it is important that

the LMS retain the potential to provide simple and flexible results.

Structurally, the LMS could also be simplified by uniting the various models into a single code.

This simplification would require the replacement of the HYDRUS executable file with the

available source code from the original HYDRUS unsaturated model. These changes would

require considerable effort but have the added advantage of removing any perceived

requirement to use a time step of a day as currently implemented within the LMS. In any case,

even if no major software redevelopment of the system is carried out, the operation of the

LMS should be further refined and streamlined to increase the overall convenience of the tool.

In the longer term, the scope of the LMS may be extended in other ways by considering, for

example, the more detailed representation required of a two- or three-dimensional

representation or the modelling of additional phenomena affecting the transport of

radionuclides and other pollutants.

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McClellan Y, August RA, Gosz JR, Gann S, Parmenter RR and Windsor M (2006). Vertical distribution, migration

rates, and model comparison of actinium in a semi-arid environment. J Environ Radioact 86 199-211,

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Merk R (2010) Numerical modeling of the water pathway for radionuclides in weakly contaminated rubble deposited

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26

SSI (1993). BIOMOVS (Biospheric Model Validation Study). Final Report. BIOMOVS Technical Report 15. Swedish

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3–13.

APPENDIX A

27

APPENDIX A Default Radionuclides

The default set of radionuclides for which data are available in the landfill modelling system

(LMS) is given in Table A1. The radionuclides were selected because of their potential

contribution to doses to workers and the public from the migration of activity to the biosphere

and for consistency with other work carried out over the years on inadvertent intrusion and

exposure to the releases of gas from a landfill site. Additional radionuclides can be added to

the system by supplying the required data.

The LEACH model only calculates the loss of the parent radionuclide from a landfill site but

the LMS supports the ingrowth of a single progeny in the first and again in the second

generation from the parent radionuclide within either the HYDRUS or TROUGH models. If the

TROUGH model is used without LEACH, additional progeny can be included in the

calculations if required. To limit the maximum time that BIOS requires to complete a run the

LMS default option is to consider just the first two generations of the radionuclide at the head

of the decay chain that are not in secular equilibrium. However, if LEACH and HYDRUS are

omitted this restriction is not enforced and a longer decay chain can be included explicitly.

Thus, for example, calculations of doses for 238

U in natural uranium generally include the

contributions from its progeny 234

U, 230

Th, 226

Ra, 210

Pb and 210

Po in secular equilibrium, while

for a pure 238

U source the contributions from the progeny in its decay chain would be taken

into account through ingrowth*. Where required, dose coefficients of a radionuclide take

account of progeny in secular equilibrium.

A1 References

Barnard RW (1993). Review of Radionuclide Source Terms used for Performance-Assessment Analyses.

SAND92-2431.

Brown J and Simmonds JR (1995). Farmland – A Dynamic Model for the Transfer of Radionuclides through

Terrestrial Foodchains. Chilton, NRPB-R273.

CEC (1988) Commission of the European Communities. Performance Assessment of Geological Isolation Systems

for Radioactive Waste (PAGIS). EUR 11775.

Egan MJ (2006). Confidence in Long-Term Radiological Safety Assessments. Implications of Alternative Models for

the Health Effects of Radiation Exposure. QRS-1265A-5.

King S (2002). Applicability of Partitioning and Transmutation to UK Wastes. NIREX Report No. DK0550 SGN912.

Reedha D and Wilmot RD (2005). Assessment Model for Disposals of Solid Low-Level Radioactive Waste in

Controlled Landfills: Case Study. SNIFFER Project UKRSRS03.

US DoE (1996) US Department of Energy. Low Level Waste Projection Program Guide.

* Previous reports using the GEOS or TROUGH models have used the notation U+238 as a shorthand reference to

the use of an extended decay chain.


28

TABLE A1 Default radionuclides included in the LMS

Radionuclide Half-life (y) Progeny* Data source

3H 1.23 10

1 Barnard, 1993; King, 2002; Reedha and Wilmot, 2005

14C 5.73 10

3 Barnard, 1993; CEC, 1988; King, 2002; Reedha and Wilmot, 2005;

US DoE, 1996

36Cl 3.01 10

5 Barnard, 1993; Egan, 2006; King, 2002; Reedha and Wilmot, 2005;

US DoE, 1996

41Ca

† 1.40 10

5 Egan, 2006

55Fe 2.70 10

0 Reedha and Wilmot, 2005

60Co 5.27 10

0 Reedha and Wilmot, 2005; US DoE, 1996

59Ni 7.50 10

7 Barnard, 1993; US DoE, 1996

63Ni 9.60 10

1 US DoE, 1996

79Se 6.50 10

4 Barnard, 1993; King, 2002; US DoE, 1996

90Sr 2.91 10

1 Egan, 2006; King, 2002; Reedha and Wilmot, 2005

94Nb 2.00 10

4 US DoE, 1996

93Zr 1.53 10

6

93mNb CEC, 1988

99Tc 2.13 10


US DoE, 1996

106Ru 1.01 10


107Pd 6.50 10

6 CEC, 1988

108mAg 1.27 10


126Sn 1.00 10

5 Barnard, 1993; Egan, 2006; King, 2002; Reedha and Wilmot, 2005

129I 1.57 10


US DoE, 1996

135Cs 2.30 10

6 Barnard, 1993; King, 2002

137Cs 3.00 10

1 US DoE, 1996; King, 2002; Reedha and Wilmot, 2005

152Eu 1.33 10

1 US DoE, 1996

154Eu 8.80 10

0 US DoE, 1996

210Pb 2.23 10

1

210Po CEC, 1988

226Ra 1.6 10

3

210Pb,

210Po Egan, 2006; King, 2002; Reedha and Wilmot, 2005; US DoE, 1996

228Ra 5.76 10

0

228Th US DoE, 1996

227Ac 2.17 10

1 Barnard, 1993; Egan, 2006; US DoE, 1996

231Pa 3.28 10

4

227Ac Barnard, 1993; US DoE, 1996

229Th 7.34 10

4 Egan, 2006

230Th 7.54 10

4

226Ra,

210Pb Barnard, 1993; Egan, 2006; King, 2002; US DoE, 1996

232Th 1.41 10

10

228Ra,

228Th Reedha and Wilmot, 2005; US DoE, 1996

233U 1.59 10

5

229Th Egan, 2006; King, 2002; US DoE, 1996

234U 2.45 10

5

230Th,

226Ra Barnard, 1993; Egan, 2006; US DoE, 1996

235U 7.04 10

8

231Pa,

227Ac Barnard, 1993; US DoE, 1996

238U 4.47 10

9

234U,

230Th Egan, 2006; King, 2002; Reedha and Wilmot, 2005; US DoE, 1996

237Np 2.14 10

6

233U,

229Th Barnard, 1993; Egan, 2006; King, 2002; US DoE, 1996

APPENDIX A

29

Radionuclide Half-life (y) Progeny* Data source

238Pu 8.77 10

1

234U,

230Th Barnard, 1993; US DoE, 1996

239Pu 2.41 10

4

235U,

231Pa Barnard, 1993; Reedha and Wilmot, 2005; US DoE, 1996

240Pu 6.54 10

3

236U,

232Th US DoE, 1996

241Pu 1.44 10

1

241Am,

237Np King, 2002; US DoE, 1996

242Pu 3.76 10

5

238U,

234U US DoE, 1996

241Am 4.32 10

2

237Np Barnard, 1993; King, 2002; Reedha and Wilmot, 2005; US DoE, 1996

242mAm 1.52 10

2

234U,

230Th CEC, 1988

243Am 7.38 10

3

239Pu,

235U CEC, 1988

244Cm 1.81 10

1

240Pu,

236U King, 2002; US DoE, 1996

* Explicitly considered progeny included in calculations. † A full plant model for

41Ca cannot yet be implemented within BIOS due to the lack of FARMLAND data

(Brown and Simmonds, 1995). It may be necessary to carry out a separate BIOS run, using a soil to plant transfer

factor rather than run the full plant compartmental for this nuclide. Alternatively, an analogue nuclide may be run

instead of 41

Ca.


30

APPENDIX B LEACH Model

The LEACH model provides a simple estimate of the activity concentration of contaminated

effluent in a landfill site commonly termed, in this context, the source zone, subject to water

ingress from infiltrating rainfall. The waste buried at the site is assumed to be uniform,

homogeneously distributed throughout the landfill site and of constant depth. On this basis the

release of activity from the waste can be simply determined by the ratio of the infiltration rate

of rainwater to the uniform thickness of the waste through which the infiltrating water must

percolate. A second inherent assumption is that the waste is subject to a broadly uniform

microporous flow of water throughout its entire extent. The uniform flow is likely to maximise

the amount of radioactive waste leached from the landfill site as the whole volume is equally

affected. In reality, there may be preferential flow channels in the waste which allow water to

reach the liner rapidly, but may cause particular volumes of the waste to remain relatively dry

for extended periods and therefore not subject to the same degree of leaching.

In LEACH the dissolution of the waste is represented by a first-order leaching process that

matches the amount lost at any time with the amount present while accounting for both decay

and sorption. The model of Baes and Sharp (1983) for the migration of contaminants through

soil assuming a constant infiltration rate is used in the model to determine the activity

concentration in the leachate. The leach rate constant λL (y–1

) is given by:

infL

landfill f

Pλ

V R

(B1)

where Pinf is the volumetric percolation rate (m3 y

–1), Vlandfill the volume of the landfill holding

the waste (m3), Rf is the retardation factor of radionuclides in the waste volume and θ is the

effective porosity of the waste if it is fully saturated, or the volumetric moisture content of the

waste if unsaturated (Rf and θ are dimensionless). Pinf and Vlandfill are given by:

inf landfill infP A I (B2)

landfill landfill landfillV A H (B3)

where Alandfill is the surface area of the landfill site (m2), Iinf is the net water infiltration rate or

Darcy flux (m y–1

) and Hlandfill (m) is the depth of the waste in the landfill site.

The retardation factor Rf is given by:

d wastef

K ρR 1

θ (B4)

where Kd is the distribution coefficient of the radionuclide in the waste (m3 kg

–1) (see Table B1,

which gives Kd values for several media) and ρwaste is the bulk density of the waste (kg m–3

).

Substituting equations (B3) and (B4) in equation (B1) gives:

landfill infinf inf

L

d hlandfill f landfill d wastelandfill landfill

A IP Iλ

K ρV R H K ρA H 1

θ

(B5)

The distribution coefficient Kd plays an important role in the rate at which the contaminant is

leached out: a lower value of Kd means a lower retardation factor and the lower the retardation

APPENDIX B

31

factor, the higher the release rate and leachate concentration. This simple model ignores

chemical kinetics and therefore does not take account of changes in the rate of dissolution

that might occur because of temperature changes or solubility thresholds.

The model also assumes that the waste has a constant saturation state, whereas in reality the

saturation state may change with depth, as water can accumulate at the bottom of the waste

site until the rate of loss matches the rate of ingress. The fully saturated fraction of the total

depth of the waste at the site may then change cyclically with the seasons. Temporal changes

in the horizon that is saturated could interact with any inhomogeneous distribution of activity

within the wastes vertical distribution. However, this issue is not likely to be significant in terms

of the timing or amount leached from the waste, as the amount lost will be bounded by the

results obtained assuming either complete saturation with minimal void spaces (see

Appendix C, Section C2) or alternatively that no puddles form and the site only maintains

residual water content. The more complex view of the landfill site, namely a perched water

table providing a head of water above an unsaturated zone that leads to an aquifer is

discussed further in Appendix C. The LEACH model only simulates the migration of a single

radionuclide from a waste site, although multiple progeny may leach from the site at distinct

rates over a considerable length of time.

If no other loss mechanisms are considered, the activity remaining in the waste at time t, I(t)

(Bq), is given by:

L- λ + λ tI t I 0 e (B6)

where I(0) is the initial activity in the source (Bq) and λ is the radioactive decay rate

constant (y–1

).

TABLE B1 Default distribution coefficients Kd for several geological media (Chen et al, 2007)

Radionuclide

Kd (m3 kg

–1)

Waste Clay Unsaturated Aquifer

3H 0 0 0 0

14C 0 0 0 0

36Cl 0 0 0 0

60Co 0 1.0 10

0 1.0 10

–1 1.0 10

–1

90Sr* 1.0 10

–2 1.0 10

–1 1.0 10

–2 1.0 10

–2

129I 0 1.0 10

–3 1.0 10

–3 1.0 10

–6

137Cs* 1.0 10

–1 1.8 10

0 2.0 10

–1 2.0 10

–1

226Ra* 5.0 10

–1 1.0 10

0 5.0 10

–1 5.0 10

–1

232Th 5.0 10

–1 5.4 10

0 1.0 10

0 1.0 10

0

238U* 1.0 10

–1 1.5 10

0 1.0 10

–2 1.0 10

–2

239Pu 2.0 10

–1 4.9 10

0 6.0 10

–1 6.0 10

–1

241Am 1.0 10

–1 8.1 10

0 7.0 10

–1 7.0 10

–1

*

Progeny in secular equilibrium are included.


32

The instantaneous contaminant flux, Fout (Bq y–1

), released from the waste at time t is

proportional to the instantaneous activity in the waste, where the constant of proportionality is

the leach rate λL. Thus:

out LF t I t (B7)

Substituting I(t) from equation (B6) gives:

L- λ + λ t

out LF t λ I 0 e (B8)

The activity concentration in the leachate at time t, Cleachate(t) (Bq m–3

), is given by:

out

leachate

inf

F tC t

P (B9)

The total activity of a particular radionuclide that leaches from a landfill in a given time t, Qout(t)

(Bq), is calculated by integrating the flux released, as given by Equation (B8), over the release

period:

L t

tL

out leachate

L0

' 'I 0 1 e

Q t C t dt

(B10)

Taking into account the containment period T (y) during which no leaching occurs, which in

this case is assumed to be the lifetime of the cap (see Section 1.2), the activity concentration

in the leachate at time t > T (OECD/NEA, 1989) is:

L t TT

L

leachate

inf

I 0 e eC t

P

(B11)

For some radionuclides, the leachate concentration in the pore fluid (ie the fluid occupying the

pore spaces in the rock or soil) is limited by its solubility. The landfill modelling system (LMS)

does not currently support limits on solubility. However, this feature could be added by

adjusting the mass balance of the contaminant in the waste using the equation (Rood, 1999):

t

t

s

1 eI t I 0 e R

(B12)

where Rs (Bq y–1

) is the solubility limited release rate during the period of interest. Rs depends

on the solubility of the radionuclide and the amount of water available and can be evaluated

using the following equation:

s s infR C P (B13)

where Cs is the solubility of the radionuclide in water (Bq m–3

).

If the activity concentration in the leachate of equations (B9) or (B11) exceeds the solubility

limit, leaching is limited by the solubility of the radionuclide. After a period of infiltration, the

radionuclide inventory is depleted sufficiently for the leachate not to exceed the solubility limit

and equations (B6), (B8), (B9), (B10) and (B11) will then apply with the leach rate then being

limited by the distribution coefficient Kd.

It is beyond the scope of the LEACH model to consider phenomena that are more complex.

For example, uranium or plutonium may form complexes with organic ligands in the waste or

APPENDIX B

33

surrounding soil. The leaching of any metal organic complexes formed depends on their

solubility, which differ from that of free metals.

B1 References

Baes CF and Sharp RD (1983). A proposal for the estimation of soil leaching and leaching constants for use in

assessment models. J Environ Qual 12 17-19.


Low Level Waste in Landfill Sites. Chilton, HPA-RPD-020.



Rood AS (1999). A Semi-Analytical Model for Assessment of the Groundwater Pathway from Surface or Buried

Contamination, Theory and User’s Manual Version 2.5. Idaho Falls, Idaho, Report No. INEEL/EXT-98-00750.


34

APPENDIX C HYDRUS Model

C1 Introduction

HYDRUS is an advanced tool for modelling the migration of water, contaminants gas flow and

heat in the partially saturated zone above the water table (Šimůnek et al, 2005). The software

is well suited to the needs of the landfill modelling system (LMS) with the caveat that it is

designed for the detailed modelling of flows over short periods and, therefore, offers time

steps of a day or less and expects any potentially time dependent input to be supplied for

times characteristic of this time step.

Section C2 provides a brief discussion on the problem of defining the partially saturated zone

and the consequences of making different assumptions with subsequent sections elaborating

on how HYDRUS can be used within the LMS. In particular, Section C5 discusses the

problem of producing a representative result from HYDRUS, which uses data and reports

results in much more detail than is required by the LMS.

C2 Flow in unsaturated media

Section 4.1 briefly introduced concepts important in the description of a partially saturated soil

where the dominant effect on the transport of water generally arises from surface interactions

between water, held in the pores and interstices of the soil, and the surrounding soil. These

microscopic interactions translate into the macroscopic matric pressure that in a partially

saturated soil is at less than atmospheric pressure and is therefore normally expressed as a

negative value with respect to atmospheric pressure. Thus, the greater the matric pressure

the greater the water content until at zero matric pressure (atmospheric pressure) the soil is

completely saturated.

The flow of water in such an unsaturated system is derived from solving Richards’ equation

(Richards, 1931), which combines Darcy’s law with the continuity equation for water and

requires that two properties of the medium are known, the unsaturated hydraulic conductivity

Kh (m s–1

) and the differential water capacity. Both of these quantities can be calculated from

the water retention curve, which gives the relationship between water content and the matric

suction or potential. This approach is analogous to the formulation under saturated flow where

the advective flux density of water* is the product of the saturated hydraulic conductivity and

the gradient of the hydrostatic head (ie the head drop per unit distance in the flow direction).

The advective flow in unsaturated sediments is the product of the unsaturated conductivity,

which varies spatially, and the total potential composed of the gravitational potential and the

matric potential (or suction) which also varies spatially. The suction gradient defines the

direction of flow from areas of low to high suction (high to low potential). As a soil is

progressively desaturated, increasing suction is required to remove the remaining water. The

hydraulic conductivity reflects the ease with which water flows through the media and

decreases with decreasing moisture saturation (ie there is greater resistance to flow when

there is a lower water content). In addition, hydraulic conductivity is also highly dependent on

soil texture. Nielsen et al (1986) noted that in unsaturated soils, in addition to water held within

* The advective flux density simply depends on the flow velocity of the water through a cross-sectional area per

unit time.

APPENDIX C

35

aggregates, immobile water, which also occurs in saturated systems, may exist in thin liquid

films around soil particles, in dead-end pores, or as relatively isolated regions, associated with

unsaturated flow. Thus, as the pathway for water flow becomes more tortuous, more of the

water held in films and small pores becomes disconnected from the flow network.

In addition to the effects on flow of water becoming disconnected within a fixed soil matrix, the

soil can also shrink and the pore space reconfigure as moisture is lost, which, for example,

may lead to cracking and the loss of integrity of clay barriers. However, for simplicity, if the

problems of cracking and compaction are ignored, a schematic representation of a typical

water retention curve for a rigid and homogeneous soil is of the form shown in Figure C1.

By definition, the volumetric water content, θ, is equal to the saturated water content, θs,

when the soil matric potential also termed the head, hm, is equal to zero. However, only

under specific circumstances is the saturated water content equal to the porosity, φ, as

entrapped air generally prevents the water content being greater than θs ≈ 0.85 φ to 0.9 φ

(Kosugi, et al, 2002).

FIGURE C1 Water retention curve of a typical soil with definitions of parameters (after Kosugi et al, 2002)

For many soils, the value of θ remains at θs for values of hm slightly less than zero. The value

of hm at which the soil starts to desaturate is defined as the air-entry value, hm,a. It is assumed

inversely proportional to the maximum pore size forming a continuous network of flow paths

within the soil. As hm decreases below hm,a, θ usually decreases according to a S-shaped

curve with an inflection point. As hm decreases further, θ decreases seemingly asymptotically

towards a soil-specific minimum water content known as the residual water content, θr. The

finite value of θr is an historical artefact of water content measurements being made in moist

soils, from which soil water retention models assumed an asymptotic form for the retention

curve at low levels of water content. As a result, most retention models only describe retention

curves in the range of θr ≤ θ ≤ θs and it is therefore often convenient to define an effective

saturation, which varies between zero and one – see equation (C3).

Relationships between the hydraulic conductivity, matric potential and water content are well

established (Jury et al, 1991; Hillel, 1998). However, as noted above, the nature of θr is still

controversial since the water content theoretically goes to zero as hm becomes infinitely

θ

s hm, a

θr

Vo

lum

etr

ic w

ate

r con

tent

θ

Air entry region

Matric head hm


36

negative. In practice, θr is treated as a fitting parameter that improves the match between

model and observation in relatively wet soils. However, because the water content

theoretically goes to zero as the matric head becomes infinitely negative, retention models

that contain θr as a fitting parameter disagree with measured data in the low matric head

range (hm < –10 m). Fayer and Simmons (1995) proposed modified parametric soil water

retention functions that adequately represent retention across the whole soil water matric

head range of 0 to –105 m, while combinations of power functions and logarithmic functions

were used by Rossi and Nimmo (1994) to characterise soil water retention from saturation to

oven-dryness. When retention and conductivity functions are coupled through mutual

parameters, the shape of the retention function has a large influence on the prediction of the

unsaturated hydraulic conductivity, especially near saturation. For example, a bimodal soil

water retention function, allowing the formulation of a secondary macroporous pore system,

may improve the predicted value of the unsaturated hydraulic conductivity in structured soils

near saturation. Finally, it should be noted that extrapolating model values outside the range

of input data for the water content and pressure head, with a negative head representing

the matric suction and a positive value a simple hydrostatic head, should only be done

with caution.

In addition to the four parameters hm,a, hm,, θs, and θr, most retention models include a

dimensionless parameter, which characterises the width of the soil pore size distribution.

Many functions have been proposed to relate the matric head to the volumetric water content;

although most of these functional relationships are empirical, some include parameters that

have a physical basis. These parameters are discussed further in the context of the

parameterisation used by HYDRUS in Section C3.

HYDRUS assumes that the upper surface has an atmospheric boundary condition. This

implies that HYDRUS should be used to model either water flow from the upper surface of the

liner including any potential puddling or from the surface of the waste site in an approach

analogous to that proposed by Merk (2010). The difference assumed in the two descriptions of

the waste is that the former is consistent with a loose packed aggregate while the latter

assumes that the waste can be characterised as a pseudo-soil without rapid finger or crack

flow (Chen et al, 2002; van Dam et al, 2004).

C2.1 Soil data

Table C1 provides an example of the data available for England and Wales at a resolution of

1 : 250,000 from the National Soil Resources Institute (NSRI) at Cranfield University. This

includes soil densities and textures, hydraulic parameters and the permanent wilting point

θpwp, which is the value of volumetric water content at which plants can no longer recover

turgidity even when placed in a saturated environment (Hillel, 1982) and characterises the

critical point at which all models shut down evaporation. The permanent wilting point is

related to the energy involved in transporting water up to the root zone and corresponds to a

very large value of the matric potential. A value of 153 m (15 bar) is widely accepted as the

characteristic value of the matric potential at the permanent wilting point for most soils

(Viterbo, 2002). Based on Cosby et al (1984), it is possible to obtain the matric potential at

the permanent wilting point for each soil type of the classification by the US Department of

Agriculture (see Section C3) using the critical review by Patterson (1990) of the

experimental estimates.

APPENDIX C

37

TABLE C1 Example of soil data available for England and Wales*

Property Example data Description

Land use PG Land use group: AR (Arable), PG (Permanent Grass), LE (Ley

Grassland) or OT (Other)

UPPER_DEPTH 20 Horizon upper depth in cm

LOWER_DEPTH 35 Horizon lower depth in cm

BULK_DENSITY 1.28 Bulk density (g cm–3

) observed

PARTICLE_DENSITY 2.63 Calculated particle density (g cm–3

)

φ 51.2 Total pore space (%) volume

θV5 16 Volumetric water content (%) at 5 kPa tension (field capacity)

θV10 11.5 Volumetric water content (%) at 10 kPa suction (equated with field

capacity in sandy soils

θV40 6.1 Volumetric water content (%) at 40 kPa suction

θV200 3.2 Volumetric water content (%) at 200 kPa suction

θpwp 1.8 Volumetric water content (%) at the wilting point (1500 kPa suction)

Ks_SV 804.1 Saturated hydraulic conductivity (sub-vertical)

KS_LAT 859.7 Saturated hydraulic conductivity (lateral)

θs 0.3401 Water content at quasi-saturation

θr 0.0085 Residual water content

α 0.1325 van Genuchten’s parameter (m–1

)

n 1.5373 van Genuchten’s parameter

m 0.3495 van Genuchten’s parameter

* http://www.landis.org.uk/data/horhydraulics.cfm

C3 HYDRUS representation and solution approach

The HYDRUS program solves Richards' equation for both saturated and unsaturated water

flow and Fickian-based advection dispersion equations for heat and solute transport using

linear finite element schemes (Šimůnek et al, 2005)*. The program may be used to analyse

water and solute movement where the unsaturated soil hydraulic properties, such as the

unsaturated hydraulic conductivity, can be described using Brooks and Corey (1964),

van Genuchten (1980) and modified van Genuchten type analytical functions with the last

form introduced to improve the description of hydraulic properties near saturation (see

Section C2). The one-dimensional transport of water and solute can be extended in any

direction with the water flow satisfying constant or time-varying head and flux boundaries

controlled, for example, by the atmospheric conditions while solute transport supports both

constant concentration and concentration flux boundary conditions. Table C2 illustrates the

default data held by HYDRUS on the 12 soil types classified by the US Department of

Agriculture (US DA) and the experimental support base for the values, as reported by the

US EPA (US EPA, 1997).

* The dispersion coefficient for solute transport includes terms that reflect the effects of molecular diffusion and

tortuosity.

http://www.landis.org.uk/data/horhydraulics.cfm


38

TABLE C2 Mean values of the van Genuchten soil water retention parameters for the 12 soil types of the US Department of Agriculture (US EPA, 1997)

Soil texture (US DA)

Saturated water content, θs

Residual water content, θr

van Genuchten parameters Saturated conductivity, Ks (m d

−1) α (m

–1) n m

Clayey soil* 0.38 0.068 0.8 1.09 0.083 4.80 10–2

Clay loam 0.41 0.095 1.9 1.31 0.237 6.24 10–2

Loam 0.43 0.078 3.6 1.56 0.359 2.50 10–1

Loamy sand 0.41 0.057 12.4 2.28 0.561 3.50

Silt 0.46 0.034 1.6 1.37 0.270 6.00 10–2

Silt loam 0.45 0.067 2.0 1.41 0.291 1.08 10–1

Silty clay 0.36 0.070 0.5 1.09 0.083 4.80 10–3

Silty clay loam 0.43 0.089 1.0 1.23 0.187 1.68 10–2

Sand 0.43 0.045 14.5 2.68 0.627 7.13

Sandy clay 0.38 0.100 2.7 1.23 0.187 2.88 10–2

Sandy clay loam 0.39 0.100 5.9 1.48 0.324 3.14 10–1

Sandy loam 0.41 0.065 7.5 1.89 0.471 1.06

* Clayey soil refers to agricultural soil with less than 60% clay.

C4 Verification and validation of HYDRUS

The user manual for version 3.0 of HYDRUS-1D (Šimůnek et al, 2005) provides evidence of

verification and validation of the code through a series of examples. Not all the examples are

directly related to the unsaturated zone represented in Figure 2; however, the examples briefly

described below are included to demonstrate the robustness of the model.

Example 1 simulated a one-dimensional laboratory infiltration experiment used as a test

problem for the UNSAT2 code (Neuman, 1972) and thus provides comparisons of the water

flow part of the HYDRUS code with results from the UNSAT2 code. The simulation was

carried out for 90 minutes, corresponding to the total time duration of the comparison. The

calculated instantaneous and cumulative infiltration rates simulated with HYDRUS agree

closely with those obtained using the UNSAT2 code.

Example 2 considered one-dimensional water flow in a field profile of the Hupselse Beck

watershed in the Netherlands. The calculations were performed for the period from

1 April to 30 September 1982, a relatively dry year. Simulation results from HYDRUS were

compared with those from the SWATRE code of Belmans et al (1983). Calculated values of

cumulative transpiration and cumulative bottom leaching were nearly identical for the

HYDRUS and SWATRE codes. The mean pressure head of the root zone simulated by

HYDRUS was very similar to that simulated by the SWATRE code, as was the level of the

groundwater table simulated over time.

Example 3 was used to verify solute transport within HYDRUS by comparing numerical results

for a problem with three solutes (NH4+, NO2

– and NO3

–) involved in a sequential first-order

APPENDIX C

39

decay reaction against results obtained with an analytical solution during one-dimensional

steady-state water flow (van Genuchten, 1985). The analytical solution holds for solute

transport in a homogenous, isotropic porous medium during steady-state unidirectional

groundwater flow. Concentration profiles for the three solutes at times of 50, 100 and

200 hours were the same for the numerical (HYDRUS) and analytical results.

Example 4 considered one-dimensional transport through Abist loam of a solute undergoing

non-linear cation adsorption. The breakthrough curve for magnesium produced using

version 6.0 of the HYDRUS software was compared with version 5.0 of the code, numerical

solutions obtained with the MONOC code (Selim et al, 1987) and experimental data. The

HYDRUS 6.0 and MONOC results were very close, showing close correspondence with the

HYDRUS 5.0 results (within around 10–15%), and a reasonable prediction of the experimental

results (the difference was between 5 and 25%). Breakthrough curves for calcium from

HYDRUS and MONOC were also in good agreement with measured data (differences were

about 10%).

Example 5 considered the movement of H3BO4 through clay loam. HYDRUS numerical results

for non-equilibrium adsorption were compared with experimental data and previous numerical

predictions assuming physical non-equilibrium and non-linear adsorption (van Genuchten,

1981), with good agreement between the three sets of results (differences were between 5

and 25%).

Example 6 (inverse analysis of outflow experiment) recorded cumulative outflow with time

from a core sample. Three hydraulic parameters were estimated by numerical inversion of the

data and from this calculation the optimised HYDRUS results for cumulative outflow against

time gave a very close match with measured results. There was very good agreement

between predicted and measured values of retention and diffusivity.

Example 7 dealt with an outflow experiment in which the pressure head in the soil sample

was measured along with the cumulative outflow while the pneumatic pressure was increased

in several small steps. Inverse analysis was used again to produce numerical results.

Excellent agreement was obtained between measured and optimised cumulative outflows and

pressure heads.

Example 8 involved an experiment in which evaporation from a core sample was measured

over time. The laboratory experiment was analysed using a revised version of Wind’s

evaporation method (Wendroth et al,1993) and soil hydraulic parameters were obtained

using the RETC code (van Genuchten et al, 1991). A close match was obtained between

analysed laboratory data and results from parameter optimisation for water retention and

hydraulic conductivity.

In addition, to ensure that the software to be used for the LMS was working correctly the

output from two of the test cases supplied with the software were compared with the outputs

given in the HYDRUS user manual (Šimůnek et al, 2005). Inspection of the results showed

matches for the relevant outputs (soil water retention and hydraulic conductivity for one test

case, and for the unsaturated hydraulic properties and pressure head at the soil surface in the

other case).


40

C5 Use of HYDRUS for disposal to landfill

The previous section illustrated that the HYDRUS model has performed well when subject to

validation and verification trials. However, HYDRUS is not designed for the modelling of waste

migration from disposal sites over hundreds or thousands of years. One of the principal

requirements of HYDRUS is information on the rainfall on a daily basis and of the initial matric

potential*. For example, Scanlon et al (2002) compared the performance of HYDRUS and

other models in an exercise which simulated water balance in warm and cold semi-arid

regions to avoid the complexity of modelling vegetative cover and, in particular,

evapotranspiration. HYDRUS performed well in this test, which is consistent with the general

approach adopted for the LMS where HYDRUS is not used to model vegetated soils.

Figure C2 provides examples of the initial matric potentials measured at the two trial sites.

Although a waste repository in the UK will not fit these semi-arid profiles the results provide an

example of the wide range of matric profiles that may occur†.

The difficulties of not having detailed data of the history of water ingress and movement at a

site is specifically discussed by Chen et al (2002) who state that despite the above difficulties,

initial flow distributions must be specified. A common approach is to assume a constant,

steady flow through the domain. By removing the effect of a drying and wetting cycle

hysteretic effects are eliminated, as well as time-varying infiltration rates at the soil surface.

Miyazaki et al (1993) assert that steady state water flow represents water moving continuously

without storage or consumption in the soil. They further state that saturated flows in

groundwater and unsaturated flows in the vadose zone, when suction is less than the air entry

value and therefore the gas phase is solely composed of entrapped air, can be considered

steady flow if the flow boundary conditions do not fluctuate‡. In the field, downward vertical

* The HYDRUS interface accepts information on rainfall on a minute-by-minute or hourly resolution but no coarser

than per day. † Until the cap and liner fail, the unsaturated zone only receives water through lateral ingress from the surrounding

area. As a one-dimensional model, this type of flow is not modelled by the LMS. ‡ If the volume of entrapped air is negligible then the soil is saturated.

FIGURE C2 Texture profiles and initial matric potentials for the two sites considered in the trial of HYDRUS and other models by Scanlon et al (2002) (copyright 2002 the American Geophysical Union, reproduced by permission of the American Geophysical Union)

APPENDIX C

41

water flows under ponded water at the soil surface and lateral flows of groundwater are typical

steady flows. However, a completely steady flow in unsaturated soil can only be generated in

the laboratory where flow boundary conditions can be fixed. Flows of water in unsaturated

soils are usually in unsteady states due to changes in the flow boundary conditions eg

variable precipitation and evaporation rates, changes in water storage in soil pores, impacts of

soil hysteresis and the consumption of soil water by plant roots. This problem is circumvented

within the LMS as HYDRUS is applied to the stage following leaching of the waste from the

packaging and its subsequent passage through the site liner into the soil below. Thus, for

example the liner may buffer the flow to smooth out the effects of rainfall variation. However,

to use HYDRUS as part of the LMS requires either an assumption for the initial matric

potential or the calculation of the matric potential assuming known rates of ingress. In the LMS

the default assumption in lieu of more specific information is to assume a constant value with

depth (Chen et al, 2007). As discussed in Section 7, the particular value chosen can have a

significant effect on any results produced.

From the above discussion, HYDRUS can be used in two ways to support LMS calculations.

Primarily, conventional LMS calculations of the solute flux can be carried out for a known or

assumed description of the matric potential for a particular soil profile. Additionally, a

preliminary calculation using the assumed water ingress into the soil can be used by HYDRUS

to calculate iteratively the equilibrium matric potential for a given soil profile. The latter option

can be generalised to accommodate time varying rates of ingress. The known short-term

seasonal variation in soil conditions and rainfall would be too detailed, in most cases, for the

broad perspective and timescales of interest to the LMS. Such a generalisation would

therefore only be relevant if modelling the effects of changes in the average rainfall in a region

over an extended period due, for example, to the effect of global warming or if looking at the

likelihood and consequences of bathtubbing events when a waste site floods and

contamination is spread over the surrounding land.

Assuming that explicit experimental information is lacking, the primary modelling of solute

transport through the unsaturated zone by the LMS can be considered in three ways. The first

option is to adopt the simpler of two assumed descriptions of the matric potential, ie a

constant negative matric potential that applies at all depths below the waste liner but above

the aquifer. At the aquifer, the carrying medium is saturated and transport calculations are

taken over by the TROUGH model as discussed in Section 5. This approach neglects any

capillary rise from the aquifer that affects the degree of saturation in the soil close to the

aquifer and leaves open the appropriate choice of matric head at the top of the unsaturated

zone immediately below the landfill liner. Previous calculations using the components of the

LMS separately have used a uniform pressure head with a matric potential of –1 m

(Chen et al, 2007). The second option is to assume that the matric potential varies uniformly

with depth so that on reaching the aquifer the soil is saturated. The assumed linear variation

of the pressure head with depth from zero pressure at the aquifer to the liner is a less severe

environment for the migration of solute, although the specification of the matric head remains

to be settled and the boundary conditions introduce other complexities (see Figure 4 and

Figure C3). The third option is to consider some approximate modelling of the water flow in

the unsaturated zone, which translates the problem from an unknown matric head to the

requirement to know or assume particular details of soil structure below the liner. This

approach would also allow the waste liner to be represented as a lens material supporting a

saturated zone above the unsaturated soil below. This latter option, discussed in Section 8.1,

would allow the soil saturation to be consistent with the amount of ingress into the site and


42

thus enable quantitative results to be produced. An additional advantage of the more

comprehensive approach would be the direct link to bathtubbing events following particular

rainfall conditions that would then be possible.

The LMS assumes that the hydraulic properties in the unsaturated zone can be represented

by the van Genuchten equation relating water content to matric head (van Genuchten, 1980):

1

m

1

n

m

1h 1

(C1)

where Θ is the dimensionless effective saturation of the soil, and α (m–1

), n and m are fitting

parameters. Parameters n and m are linked by the equation:

1m 1

n (C2)

The effective saturation of the soil, Θ, is given by:

r

s r

(C3)

where θs is the saturated water content and θr is the residual water content.

Applying the default LMS parameterisation to the above equation gives the retention curve

shown in Figure C3 and labelled LMS default. Figure C3 also shows example curves derived

from the data of Table C2.

FIGURE C3 Effective saturation as a function of pressure head, shown for the default LMS van Genuchten parameter values and those of a selection of standard soils from Table C2

APPENDIX C

43

FIGURE C4 Variation in timing and magnitude of the predicted 129

I flux released from a waste site matching the Sniffer defaults for a variety of initial matric head suctions and lower boundary conditions. The matric head hm (m) is either constant with depth or increases uniformly with increasing depth until matching the zero matric head of the aquifer at the depth of the aquifer, as indicated by the free draining label

The variation in pressure head with depth translates into a variation in the water content and

hydraulic conductivity. Figure C4 shows the effect on the final flux of 129

I estimated by the LMS

to leave the aquifer when emulating the Sniffer scenario discussed in Section 7.1 under

conditions of either constant matric pressure or a pressure head that varies linearly between

the liner and the aquifer.

Figure C4 displays the expected trend with greater saturation, indicated by a less negative

pressure head, resulting in a larger peak flux occurring earlier. A similar, but less dramatic

effect occurs if the matric potential between the waste site and the aquifer is assumed to vary

linearly from a negative value at the base of the waste liner to a fully saturated zero pressure

head at the top of the aquifer as indicated by the free draining label in Figure C4. Linearly

varying the matric potential with depth from the initial value to zero lowers the peak flux, when

compared to maintaining a constant initial matric potential throughout the unsaturated zone,

but advances it in time. This reflects the shorter travel time required because of the increase

in water content with depth, while the increase in spatial dispersion with depth results in the

lower peak flux. A uniform reduction in the level of saturation slows down the flux allowing

temporal dispersion to reduce and broaden the peak. The very long half-life of 129

I (1.57 107 y)

combined with the radionuclide’s high mobility means that radioactive decay plays very little

part in diminishing the peak flux. A low saturation environment has a much greater effect on

radionuclides that are less mobile and have shorter half-lives. Errors in the estimation of the

level of soil saturation could have a very large impact on the predicted flux.

102 103 104 105 106

-hm(0)

-hm(0.01)

-hm(0.1)

-hm(1)

-hm(10)

-hm(0.1) free draining

-hm(1) free draining

Saturated no HYDRUS

1012

1015

1018

Flu

x (

ato

ms y

-1)

Time (years)


44

Figure C4 also shows how the flux is estimated to vary if the HYDRUS component of the LMS

calculation is replaced by a saturated layer modelled using TROUGH. The difference between

this result and the calculation made for a fully saturated system using HYDRUS is a measure

of the likely discrepancy between the results with and without water balance in the

implementation of HYDRUS within the LMS.

C6 References

Belmans C, Wesseling JG and Feddes RA (1983). Simulation model of the water balance of a cropped soil:

SWATRE. J Hydrol 63 271-286.

Brooks RH and Corey AT (1964). Hydraulic Properties of Porous Media, Hydrology Paper 3. Colorado State

University, Fort Collins CO, pp 1–15.

Chen J-S, Drake RL, Lin Z and Jewett DG (2002). Simulating Radionuclide Fate and Transport in the Unsaturated

Zone: Evaluation and Sensitivity Analyses of Select Computer Models. EPA/600/R-02/082


Low Level Waste in Landfill Sites. Chilton, HPA-RPD-020.

Cosby BJ, Hornberger GM, Clapp RB and Ginn TR (1984). A statistical exploration of the relationships of soil

moisture characteristics to the physical properties of soils. Water Resources Res 20 682-690.

Fayer MJ and Simmons CS (1995). Modified soil water retention functions for all matric suctions. Water Resources

Res 31 1233-1238.

Hillel D (1982). Introduction to Soil Physics. San Diego CA, Academic Press.

Hillel D (1998). Environmental Soil Physics. San Diego CA, Academic Press.

Jury WA, Gardner WR and Gardner WH (1991). Soil Physics. New York NY, John Wiley and Sons Inc.

Kosugi K, Hopmans JW and Dane JH (2002). Water Retention and Storage – Parametric Models. IN: Methods of Soil

Analysis. Part 4. Physical Methods. (JH Dane and GC Topp, Eds). Soil Science Society of America Book Series

No. 5, pp 739-758.

Merk R (2010) Numerical modeling of the water pathway for radionuclides in weakly contaminated rubble deposited

after clearance. Proceedings of Third European IRPA Congress 2010 June 14−18, Helsinki, Finland.

Miyazaki T, Hasegawa S and Kasubuchi T (1993). Water Flow in Soils. New York NY, Marcel Dekker Inc.

Neuman SP (1972). Finite Element Computer Programs for Flow in Saturated-Unsaturated Porous Media, Second

Annual Report, Project No A10-SWC-77.

Nielsen DR, van Genuchten MT and Biggar JW (1986). Water flow and solute transport processes in the unsaturated

zone. Water Resources Res 22 895-1085.

Patterson KA (1990). Global Distribution of Total and Total-Available Soil Water-Holding Capacities. MSc Thesis,

University of Delaware, 119.

Richards LA (1931). Capillary conduction of liquids through porous media. Physics 1 318-333.

Rossi C and Nimmo JR (1994). Modeling of soil water retention from saturation to oven dryness. Water Resources

Res 30 701-708.

Scanlon BR, Christman M, Reedy RC, Porro I, Šimůnek J and Flerchinger GN (2002). Intercode comparisons for

simulating water balance of surficial sediments in semiarid regions. Water Resources Res 38(12) 59-1–59-16,

doi: 10.1029/2001WR001233.

Selim HM, Schulin R and Flühler H (1987). Transport and ion exchange of calcium and magnesium in an aggregated

soil. Soil. Sci Soc Am J 51(4) 876-884.

Šimůnek J, van Genuchten MT and Sejna M (2005). The HYDRUS-1D Software Package for Simulating the One-

Dimensional Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media. Version 3.0, HYDRUS

Software Series 1, Department of Environmental Sciences, University of California Riverside, Riverside CA,

270 pp.

US EPA (1997). User’s Guide for the Johnson and Ettinger (1991) Model for Subsurface Vapor Intrusion Into

Buildings, PN 5099-6.

van Dam JC, De Rooij GH, Heinen M and Stagnitti F (2004). Concepts and dimensionality in modeling unsaturated

water flow and solute transport. In Wageningen UR Frontis Series, Volume 6, Unsaturated-zone Modeling:

Progress, Challenges and Applications (RA Feddes et al, Eds), 364 pp.

van Genuchten, MTh (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil

Sci Soc Am J 44(935) 892-898.

van Genuchten MTh (1981). Non-Equilibrium Transport Parameters from Miscible Displacement Experiments.

US Salinity Laboratory, Riverside CA. Research Report No. 119.

APPENDIX C

45


reactions. Comput Geosci 11(2) 129–147.

van Genuchten MTh, Leij FJ and Yates SR (1991). The RETC Code for Quantifying the Hydraulic Functions of

Unsaturated Soils. Report No. EPA/600/2-91/065.

Viterbo P (2002). A Review of Parameterization Schemes for Land Surface Processes. ECMWF, Shinfield Park,

Reading, England Meteorological Training Course Lecture Series (European Centre for Medium Range Weather

Forecasting).

Wendroth O, Ehlers W, Hopmans JW Kage H, Halbertsma J and Wösten JHM (1993). Reevaluation of the

evaporation method for determining hydraulic functions in unsaturated soils. Soil Sci Soc Am J 57 1436-1443.


46

APPENDIX D Comparison of the TROUGH Model with Analytical Results

The performance of the geosphere model TROUGH, a key component of the landfill modelling

system (LMS), was directly assessed by comparing results from TROUGH with the

corresponding results calculated using an exact analytical model. In the first instance the

three deterministic examples of the PSACOIN level E study, prepared by the PSAC User

Group (OECD/NEA, 1989), were compared with the predictions of TROUGH. This simple

comparison was then extended by using the analytical model CHAIN (van Genuchten, 1985)

to provide a more comprehensive test of the adequacy of TROUGH.

D1 Comparison of TROUGH with the analytical solution of PSACOIN level E

The scenarios of the PSACOIN level E study (OECD/NEA, 1989) simulate deep geological

disposal within the limits imposed by the analytical solution of Robinson and Hodgkinson

(1987). This simple screening model, which includes the most important aspects of

radionuclide migration, contains components representing the source term and geosphere

transport for both single radionuclides and, under limited circumstances, radionuclides that are

part of a decay chain. The analytical solution assumes that after a delay the primary

containment fails and allows the radionuclides to leach from the waste following the ingress of

water. The released radionuclides are then transported through a two-layer geosphere by

groundwater, with the geological layers defined by their hydrogeological properties (eg path

length, flow velocity, sorption and dispersivity). Finally, the radioactivity is released into a

simple biosphere consisting of a dilution model of drinking water and doses from the ingestion

of drinking water are calculated. Two radionuclides were considered: 129

I and 237

Np with

progeny 233

U and 229

Th. The parameter values required to represent the three cases in the

PSACOIN level E study, including a description of the two layers, called layer A and layer B,

are given in Table D1. The flux at the inlet boundary is considered to be a purely advective

flux with no diffusive flux and the size of the spatial grid used in TROUGH is set to be half of

the dispersive length of the layer.

TROUGH and the analytical model have identical initial fluxes entering the first layer of the

geosphere (layer A) for each radionuclide and case considered. However, on traversing the

first geological layer the peak flux and the time at which the peak occurs no longer match for

any of the cases and radionuclides, although the differences between the results are small.

Estimates of peak flux and peak time at the end of the first layer of TROUGH and the exact

results of the analytical formulation are shown in Table D2. The comparison shows the original

values calculated by TROUGH in the PSACOIN level E study and the values derived using

the TROUGH component model of the LMS. The differences between the original and LMS

results are predominately the result of changes in the step size used, which allow the peak

flux and time to be more accurately determined.

Table D2 illustrates that in all cases, the error in the peak flux calculated by the TROUGH

component of the LMS at the end of layer A of the geosphere is less than 1.5% and the error

in the timing of the peak flux is less than 2.3%. In addition, there are no marked differences in

performance between the three scenarios. Differences between TROUGH results for the

original PSACOIN level E intercomparison and analytical results are generally higher but are

still considered to be acceptable for the LMS. The maximum errors are 23% and 44%,

APPENDIX D

47

TABLE D1 Parameter values used for TROUGH calculations of PSACOIN level E cases (OECD/NEA, 1989)

Parameter Case 1 Case 2 Case 3

Delay before leaching starts (y) 1 102 3 10

2 1 10

3

Release rate (y–1

) 129

I 1 10–2

3 10–3

1 10–3

237Np 1 10

–5 3 10

–6 1 10

–6

233U 1 10

–5 3 10

–6 1 10

–6

229Th 1 10

–5 3 10

–6 1 10

–6

Source term (mol) 129

I 1 102 1 10

2 1 10

2

237Np 1 10

3 1 10

3 1 10

3

233U 1 10

2 1 10

2 1 10

2

229Th 1 10

3 1 10

3 1 10

3

Groundwater velocity (m y –1

) Layer A 1 10–1

5 10–2

3 10–2

Layer B 1 10–1

3 10–2

1 10–2

Dispersion length (m) Layer A 1 101 1 10

1 1 10

1

Layer B 5 100 5 10

0 5 10

0

Geosphere path length (m) Layer A 1 102 2 10

2 5 10

2

Layer B 5 101 1 10

2 2 10

2

Retardation factor (–) Layer A 129

I 1 100 3 10

0 3 10

0

237Np 3 10

2 5 10

2 8 10

2

233U 3 10

1 5 10

1 8 10

1

229Th 3 10

2 5 10

2 8 10

2

Layer B 129

I 1 100 3 10

0 3 10

0

237Np 3 10

2 1 10

3 8 10

2

233U 3 10

1 1 10

2 8 10

1

229Th 3 10

2 1 10

3 8 10

2

Receiving stream flow (m3 y

–1) 3 10

5 1 10

6 3 10

6

respectively, which reflect the use of a more refined time step in the LMS calculations.

Two other minor factors that may have slightly affected the results are that the LMS version of

the pre-processor used by TROUGH calculates the rate of progeny ingrowth more accurately

and that the mechanism for handling the terminal boundary condition is slightly different*.

Table D3 shows the predicted peak doses received from drinking water abstracted from the

aquifer at the end of layer B of the geosphere and the timing of the doses as estimated by

TROUGH and the corresponding values determined by the analytical solution. As might be

expected, after allowing for the effect of the additional distance through which radionuclides

are transported the error in the doses estimated for the LMS calculations are generally slightly

* The numerical precision of the calculation of ingrowth of progeny was increased to improve the estimates of the

initial progeny fluxes. Instead of applying a particular TROUGH boundary condition option an extra-long terminal

layer is added with properties that match those of the actual end layer to avoid any anomalous boundary effects

in the estimated end layer flux.

TABLE D2 Comparison of peak times and peak fluxes on leaving layer A calculated by TROUGH with analytical results

Radionuclide

Analytical results TROUGH estimates Error with analytical result (%)*

Peak time (y)

Peak flux (mol y

–1)

Peak time (y) Peak flux (mols y–1

) Peak time Peak flux

LMS PSACOIN LMS PSACOIN LMS PSACOIN LMS PSACOIN

Case 1

129I 9.55 10

2 1.06 10

–1 9.71 10

2 9.75 10

2 1.06 10

–1 1.00 10

–1 –1.62 –2.09 0.30 5.66

237Np 3.07 10

5 2.52 10

–3 3.06 10

5 3.11 10

5 2.55 10

–3 2.46 10

–3 0.26 –1.30 –1.42 2.38

233U 5.24 10

4 6.95 10

–4 5.16 10

4 7.51 10

4 7.01 10

–4 6.93 10

–4 1.50 –43.32 –0.86 0.29

229Th 6.63 10

4 3.12 10

–6 6.53 10

4 8.42 10

4 3.15 10

–6 3.10 10

–6 1.45 –27.00 –0.91 0.64

Case 2

129I 1.10 10

4 1.16 10

–2 1.08 10

4 1.10 10

4 1.17 10

–2 1.13 10

–2 1.40 0.00 –0.74 2.59

237Np 1.92 10

6 3.22 10

–4 1.90 10

6 1.99 10

6 3.21 10

–4 2.84 10

–4 0.99 –3.65 0.14 11.80

233U 1.12 10

6 1.48 10

–4 1.11 10

6 1.10 10

6 1.50 10

–4 1.45 10

–4 0.99 1.79 –1.44 2.03

229Th 1.12 10

6 6.86 10

–7 1.10 10

6 1.17 10

6 6.96 10

–7 6.75 10

–7 1.88 –4.46 –1.43 1.60

Case 3

129I 4.91 10

4 4.14 10

–3 4.87 10

4 4. 88 10

4 4.16 10

–3 3.98 10

–3 0.87 0.61 –0.44 3.86

237Np 1.17 10

7 2.53 10

–6 1.14 10

7 1.29 10

7 2.53 10

–6 1.95 10

–6 2.26 –10.26 –0.15 22.92

233U 9.17 10

6 3.14 10

–6 8.97 10

6 9.64 10

6 3.18 10

–6 3.00 10

–6 2.19 –5.13 –1.24 4.46

229Th 9.17 10

6 1.46 10

–8 8.98 10

6 9.64 10

6 1.48 10

–8 1.39 10

–8 2.08 –5.13 –1.25 4.79

*

Error = (Analytical result – TROUGH result) / Analytical result.

TABLE D3 Comparison of peak times and peak doses from drinking water abstracted from the aquifer at the end of layer B calculated by TROUGH with analytical results

Radionuclide

Analytical results TROUGH estimates Error with analytical result (%)*

Peak time (y)

Peak dose (Sv y

–1)

Peak time (y) Peak dose (Sv y–1

) Peak time Peak dose

LMS PSACOIN LMS PSACOIN LMS PSACOIN LMS PSACOIN

Case 1

129I 1.47 10

3 1.22 10

–5 1.48 10

3 1.45 10

3 1.22 10

–5 1.18 10

–5 –0.61 1.36 0.02 3.28

237Np 4.62 10

5 3.54 10

–5 4.58 10

5 4.35 10

5 3.59 10

–5 3.53 10

–5 0.78 5.84 –1.60 0.28

233U 6.95 10

4 9.21 10

–6 6.84 10

4 7.5110

4 9.28 10

–6 8.82 10

–6 1.58 –8.06 –0.81 4.23

229Th 8.33 10

4 1.27 10

–5 8.14 10

4 8.42 10

4 1.28 10

–5 1.26 10

–5 2.31 –1.08 –0.81 0.79

Case 2

129I 2.10 10

4 3.49 10

–7 2.07 10

4 2.05 10

4 3.48 10

–7 3.46 10

–7 1.42 2.38 0.05 0.86

237Np 4.86 10

6 3.22 10

–7 4.78 10

6 4.75 10

6 3.20 10

–7 3.16 10

–7 1.61 2.26 0.47 1.86

233U 3.43 10

6 2.07 10

–7 3.35 10

6 3.30 10

6 2.10 10

–7 2.05 10

–7 2.44 3.79 –1.43 0.97

229Th 3.43 10

6 2.94 10

–7 3.36 10

6 3.30 10

6 2.98 10

–7 2.90 10

–7 2.15 3.79 –1.41 1.36

Case 3

129I 1.08 10

5 3.23 10

–8 1.07 10

5 1.06 10

5 3.34 10

–8 3.28 10

–8 0.74 1.85 –3.26 –1.55

237Np 2.45 10

7 2.59 10

–11 2.41 10

7 2.45 10

7 2.60 10

–11 2.39 10

–11 1.81 0.00 –0.44 7.72

233U 2.12 10

7 3.60 10

–11 2.07 10

7 2.07 10

7 3.64 10

–11 3.54 10

–11 2.31 2.36 –1.30 1.67

229Th 2.12 10

7 5.10 10

–11 2.07 10

7 2.09 10

7 5.16 10

–11 5.02 10

–11 2.31 1.42 –1.32 1.57

* Error = (Analytical result – TROUGH result) / Analytical result.


50

greater than the corresponding flux error at the end of layer A, although differences are

marginal. The dose contribution calculated for each radionuclide at the end of layer B is a

direct proxy for the flux at the interception point and the differences between the original

PSACOIN level E study and new LMS results are likely to be predominately due to changes

in the step size used in the TROUGH calculations of the flux.

D2 Comparison of TROUGH with the model CHAIN

An analytical solution for a single layer system supporting a decay chain of up to four

radionuclides has been published by van Genuchten (1985). A software program, called

CHAIN, produced by van Genuchten evaluates the solution for various parameter and

radionuclide combinations and allows a detail comparison to be made with results produced

by TROUGH.

Figure D1 summarises the results of a test carried out using the case 1 scenario of the

PSACOIN level E exercise for 129

I. It shows that there is a close match between the results

produced by CHAIN and TROUGH. A test was also conducted to compare the sequential use

of TROUGH with the use of TROUGH in two-layer mode under conditions when little

difference is expected between the sequential and two-layer approaches. Figure D1

illustrates, for the particular boundary conditions chosen, the excellent agreement between

TROUGH run separately as two consecutive layers with the output of the first (layer A)

supplying the second (layer B) and the TROUGH results from a single two-layer calculation.

The results for layer A are also in good agreement with the results from the analytical model

CHAIN. Table D3 shows that the result of the analytical model CHAIN agree with those from

layer B of TROUGH.

Fluxes calculated using TROUGH with a single layer geosphere for 239

Pu and three

radionuclides in its decay chain (235

U, 231

Pa and 227

Ac) were also compared with those

calculated by the CHAIN model for the same general PSACOIN scenario. The results, shown

in Figure D2, illustrate that TROUGH can successfully reproduce the flux of the analytical

model over the majority of the temporal extent of the breakthrough curve for each of the four

radionuclides considered in the 239

Pu chain, although TROUGH allows a small amount of flux

to traverse the barrier more quickly than predicted by the analytical result.

The outcome of the intercomparison exercise with the model CHAIN demonstrates that

TROUGH can produce results that are in very good agreement with independent analytical

formulations.

D3 References



Robinson PC and Hodgkinson DR (1987). Exact solutions for radionuclide transport in the presence of parameter

uncertainty. Radioact Waste Man Nucl Fuel Cycle 8(4) 283-311.


reactions. Comput Geosci 11(2) 129-147.

APPENDIX D

51

FIGURE D1 Comparison of fluxes of 129

I calculated by TROUGH for case 1 of the PSACOIN study with the results of the analytical model CHAIN

Figure D2 Comparison of the flux of 239

Pu and three radionuclides in its decay chain (235

U, 231

Pa and

227Ac) calculated by TROUGH with a single layer geosphere for case 1 of the PSACOIN study

with the results of the analytical model CHAIN

0 500 1000 1500 2000 2500

0.000.020.040.060.080.10

0.000.020.040.060.080.10

0.000.020.040.060.080.10

0.000.020.040.060.080.10

TROUGH single layer A

TROUGH single layer B

TROUGH 2 layer calculation

CHAIN with and without delay

Flu

x o

f 129I (m

ol y

-1)

Time (years)

101 102 103 104 105 106 107

Time (years)

10-20

10-15

10-10

10-5

10010-20

10-15

10-10

10-5

100

Flu

x a

fter

500 m

of aquifer

(mol y

-1)

Solution: chain

Solution: Trough

239Pu

235U231Pa

227Ac

101 102 103 104 105 106 107

Time (years)

10-20

10-15

10-10

10-5

10010-20

10-15

10-10

10-5

10010-20

10-15

10-10

10-5

10010-20

10-15

10-10

10-5

100

Flu

x a

fter

500 m

of aquifer

(mol y

-1)

239Pu

235U

231Pa

227Ac


52

APPENDIX E WELL Model

The landfill modelling system (LMS) includes a simple model to calculate the peak annual

dose from drinking water abstracted from a well using a variant of a similar BIOS calculation

developed to assess the dose from drinking river water (see Section F2). This dose is

proportional to the activity concentration in the water, assumed uniform across the aquifer, at

a particular downstream location at a time when it leads to the highest annual dose. The peak

committed effective dose rate from drinking filtered well water, Dwater (Sv y–1

), is given by:

water water fil water ingD C R I DC (E1)

where Cwater is the peak activity concentration in aquifer water (Bq m–3

) averaged over a year,

Iwater is the ingestion rate of water (m3 y

–1) (Smith and Jones, 2003), DCIng is the ingestion

dose coefficient (Sv Bq–1

) (ICRP, 1996) and by extension of the approach used in BIOS for

river modelling (see Section F2) Rfil is the fraction in filtered well water given by:

fil

d

1R

1 K SSL

(E2)

where SSL is the suspended sediment load in well water (10–2

kg m–3

) and Kd is the sediment

partition coefficient (m3 kg

–1). Cwater is given by:

TROUGH 1/2 landfill landfillwater

aquifer aquifer aquifer

F T W L C =

A W H v (E3)

where FTROUGH is the peak radionuclide flux from the aquifer into a well over a period of a year

(atoms y–1

), T1/2 is the radioactive half-life (y–1

), W landfill (m) and Llandfill (m) are the width and the

length of the landfill, respectively. Aaquifer is the area of the aquifer (assumed to be 1 m2), and

Waquifer (m) and Haquifer (m) are the effective width and the thickness of the aquifer, respectively,

while v is the flow rate of the pore water in the aquifer (m y–1

) and θ is the dimensionless

effective porosity of the aquifer.

The mixing zone of the leachate in the aquifer, within a 250 m travel distance of the source, is

limited to the top part of the aquifer; a transverse dispersivity of 1% of the travel length is

assumed, giving a mixing zone of around 2.5 m (Ingebritsen et al, 2006). However, when the

groundwater is abstracted, it is assumed that the radioactivity in the water abstracted at the

well is mixed with water abstracted over the entire thickness of the aquifer. This has the effect

of diluting the activity by the volumetric flow over the effective width of the aquifer.

E1 References

ICRP (1996). Age Dependent Doses to Members of the Public from Intakes of Radionuclides: Part 5 Compilation of

Ingestion and Inhalation Dose Coefficients, ICRP Publication 72. Ann ICRP, 26(1).

Ingebritsen SE Sanford WE and Neuzil CE (2006). Groundwater in Geologic Processes, 2nd Edition. Cambridge

University Press.

Smith KR and Jones AL (2003). Generalised Habit Data for Radiological Assessments. Chilton, NRPB-W41.

APPENDIX F

53

APPENDIX F Comparison of LMS with an Unpublished Assessment

To support the verification of the landfill modelling system (LMS) a comparison was made

with selected results previously calculated in an unpublished assessment of the radiological

impact of disposal to landfill of small quantities of solid radioactive waste (Cabianca et al,

to be published). The unpublished assessment used an alternative geosphere model GEOS

(Hill, 1989) instead of TROUGH and version 4A of the BIOS model, which is an earlier but

essentially equivalent version of the BIOS_4B model implemented in the LMS

(see Section F2). The unpublished assessment considered ranges of values for the

release coefficient and other key variables in an uncertainty analysis as well as using best

estimate parameter values. However, only some of the best estimate results from the

previous unpublished assessment are compared with the corresponding LMS predictions in

this appendix.

F1 Comparison of the GEOS model with TROUGH

The GEOS model (Hill, 1989)*, developed by the then National Radiological Protection

Board†, is similar to TROUGH in its representation of migration through a one-dimensional

geosphere with multiple layers. The model predicts the transport of radionuclides with pore

water in rocks and includes the processes of advection, dispersion, radioactive decay and

absorption on to rocks. The model assumes that radionuclides are released into the saturated

zone or aquifer at a fixed rate that is dependent on an element-specific release coefficient and

the quantity of water flowing through the landfill.

The intercomparisons are based on the generic waste site representative of a site for

hazardous waste described, in the unpublished assessment of the radiological impact of

disposal to landfill of small quantities of solid radioactive waste, as type C. Modelling of the

unsaturated zone was omitted. The site has the general structure shown in Figure 2 with the

parameters characterising the cap barriers and waste, including element-dependent

parameters, given in Tables F1 and F2.

Table F2 provides the distribution coefficient values used by the unpublished assessment for

deterministic calculations. The Kd values in Table F2 can be assumed to be the same as the

best estimate values of a probability distribution, if the deterministic value is greater than zero.

Deterministic values represent the most likely values and are generally the distribution-

weighted mean of the appropriate ranges. In the unpublished assessment, if the deterministic

Kd value was zero (ie if it the radionuclide was not sorbed on to sediments) the probability

distribution used in the uncertainty analysis was assumed to be a beta distribution with a

range between zero and ten‡.

* This GEOS model should not be confused with the model of the same name developed by Ferry (1996). † In 2005 the NRPB was incorporated into the Health Protection Agency (HPA). On 1 April 2013 the HPA was

abolished and its staff and functions transferred to Public Health England. ‡ No information is given in the unpublished assessment on the value of the two parameters used to specify the

particular form of the beta distribution used, which can vary in shape from forms similar to right and left skewed

lognormals to straight lines. However, it may be assumed that the form selected would confine the extent of

significant probability to a small region near the origin with a residual asymptotic tail.


54

TABLE F1 Characteristics of type C (hazardous) landfill site used in the intercomparison between GEOS and TROUGH

Parameter Value

Volume (m3) 2 10

6

Area (ha) 2 101

Average depth (m) 1 101

Waste density (t m–3

) 7.5 10–1

Total activity disposed (Bq) 1 1010

Lifetime (y) 1.5 101

Rain ingress (m y–1

) 3 10–1

Volumetric flow rate of the aquifer (m3 y

–1) 1 10

6

Layer 1 Clayey subsoil (m) 5 100

Layer 2 Sandy aquifer (m) 5 102

TABLE F2 Release, distribution and retardation coefficients in clay and a sand aquifer used in the intercomparison between GEOS and TROUGH

Element

Distribution coefficient, Kd (m

3 t–1

)

Retardation coefficient*

Release coefficient Clay Sand aquifer Clay Sand aquifer

C 0 0 1 100 1 10

0 9 10

–2

Cl 0 0 1 100 1 10

0 3 10

–1

Pb 6 103 2 10

2 4 10

4 1 10

3 2 10

–3

Ra 7 101 5 10

2 5 10

2 3 10

3 2 10

–3

Ac 3 103 6 10

2 2 10

4 3 10

3 2 10

–3

Th 1 104 2 10

3 7 10

4 1 10

4 4 10

–4

Pa 6 102 5 10

2 4 10

3 3 10

3 3 10

–3

U 4 102 5 10

1 2 10

3 3 10

2 1 10

–3

Pu 4 103 6 10

2 3 10

4 3 10

3 3 10

–4

Am 3 103 7 10

2 2 10

4 4 10

3 3 10

–3

* The retardation coefficient was calculated assuming a bulk density of 2.0 t m–3

and a porosity of 0.3 in clay and

0.35 in sand.

The unpublished assessment of the radiological impact of disposal to landfill of small

quantities of solid radioactive waste does not provide best estimate values derived from a

probability distribution for the Kd values assumed to be zero in Table F2. Calculations by the

LMS using the parameter values of Table F2 were therefore unable to reproduce accurately

the best estimate results of the unpublished assessment as the Kd values used in the

GEOS calculations were not reported if the corresponding deterministic value in Table F2

was zero.

APPENDIX F

55

F1.1 Comparison of doses from ingestion of well water

The use of well water from an aquifer close to a landfill is likely to be a significant exposure

pathway. Although the well may not directly disrupt the waste, it is likely to shorten the migration

path for radionuclides in groundwater, potentially leading to higher activity concentrations in

drinking water and hence higher doses. The unpublished assessment assumed that individuals

obtain all their drinking water from the well and that the water is of sufficient quality not to need

filtering. Although the LMS assumes by default that well water is filtered, this assumption was

not used in the comparison. The total activity released to the aquifer each year, Aaquifer, was

calculated for a number of radionuclides typically disposed of to landfill using the TROUGH

model and the resultant ingestion doses were compared with the calculations carried out using

GEOS. The comparison was based on the estimated peak dose, calculated using a combined

activity released to the aquifer of all the progenies in the decay chain, suitably weighted to take

account of the contribution to the dose from ingestion of the progeny.

The doses from ingestion of drinking water were calculated using the equation:

aquifer water

water

aquifer

R ID

V (F1)

where Raquifer is the radiologically weighted release (Sv y–1

), Iwater is the quantity of water

ingested in a year (0.6 m3 y

–1 for adults) (Smith and Jones, 2003) and Vaquifer is the volumetric

flow rate in the aquifer (m3 y

–1).

The radiologically weighted release Raquifer is given by:

aquifer ing,i aquifer,i

i

R DC A (F2)

where Aaquifer is the activity released to the aquifer (Bq y–1

) of the ith radionuclide in the decay

chain and DCing,i is the dose coefficient of the same radionuclide (Sv Bq–1

) (ICRP, 2001).

Doses from ingestion of drinking water from a well provided in the report of the unpublished

assessment cannot be compared directly with those calculated by the LMS as they are based

on the estimated maximum flux of a radionuclide into the underlying aquifer, while the

appropriate deterministic parameters to reproduce the calculation are not reported. However,

by applying the same methodology the best estimate activity concentrations from the GEOS

calculations can be used to generate a set of doses that can be compared to those produced

by the LMS using the deterministic parameters provided, as shown in Table F3. The lower

peak doses at longer times for the GEOS estimates for 14

C and 36

Cl in comparison to those of

the LMS are a consequence of using non-zero distribution coefficient values in the best

estimate calculation (see Table F2). These particular calculations are therefore not directly

comparable, although the lower dose predicted by the GEOS estimates is an expected

consequence of partial sorption. The remaining calculations are in good agreement with the

worst differing by approximately a factor of two.

F2 BIOS model

BIOS is a compartmental model, used to simulate the dispersion of radioactivity in the

biosphere. The main compartments represent deep and surface soils, rivers and seas (Martin

et al, 1991). BIOS calculates activity concentrations in environmental media and the doses


56

TABLE F3 Comparison of the deterministic and best estimate doses from ingestion of drinking water calculated by the LMS and GEOS

Radionuclide

GEOS LMS

Peak time (y) Dose (Sv y–1

) Peak time (y) Dose (Sv y–1

)

14C 1.40 10

2 9.0 10

–10 1.22 10

2 7.5 10

–9

36Cl 1.13 10

2 4.6 10

–9 9.83 10

1 3.1 10

–8

226Ra 1.42 10

4 1.2 10

–11 1.59 10

4 1.8 10

–11

232Th 2.45 10

6 5.2 10

–9 2.24 10

6 5.5 10

–9

235U 2.13 10

5 1.4 10

–8 1.48 10

5 3.2 10

–8

238U 4.35 10

5 7.1 10

–9 2.14 10

5 9.6 10

–9

239Pu 2.44 10

5 4.7 10

–13 2.03 10

5 7.5 10

–13

likely to result following discharges into rivers or deep soil from an aquifer. The soil

components represent farmland near to a river or lake that may be contaminated by irrigation

or by a direct upwelling of radionuclides into the soil on which animals are raised and crops

are grown. In BIOS a coupled set of linear first-order differential equations represent the

transfer of radioactivity between various model compartments. Transfer rates represent the

various processes described by the model, such as the uptake of radionuclides from soils and

grasses and are calculated from available equilibrium data as described in Martin et al (1991)

and Smith and Simmonds (2009). Element-dependent equilibrium transfer factors are also

used to predict the concentrations of radionuclides in freshwater fish.

Figures F1 to F4 show different components of the BIOS model. Figure F1 shows the

terrestrial biosphere model that includes a river and a lake, and the interactions with the

associated arable and pasture compartments. The size of the lake, the number of river

segments and branches can be specified to transform the generic model to fit a particular

assessment. Figure F2 shows the BIOS soil model for both arable and pasture land, while

Figure F3 shows a typical plant model for green vegetables including transfer processes

representing uptake via irrigation and root uptake from arable soil. Finally, Figure F4 shows

the BIOS pasture model linking into the pasture soil model. When appropriate, slight

modifications are introduced to these models to account for the fixation of caesium.

F2.1 Comparison of doses calculated by BIOS_4A and BIOS_6B

The BIOS model has evolved over a number of years and a number of different versions

have been produced. Each new version has been compared with the previous version and

other independent models (see Section 6.1.1). However, to provide additional credibility to

the intercomparison between the LMS and calculations using a combination of the GEOS

and BIOS_4A models, a direct comparison between BIOS_4A and BIOS_6B is provided in

Table F4 for a continuous release of 1 MBq y–1

.

As shown in Table F4 the doses calculated by BIOS_4A are generally in very good

agreement with those calculated for 99

Tc and 235

U by BIOS_6B the version included in the

LMS. This level of agreement between the latest and earlier versions of the BIOS model

indicates that, although BIOS_6B is implemented using different solution methods and

software, the underlying conceptual models have been consistently interpreted.

APPENDIX F

57

FIGURE F1 Generic terrestrial and aquatic biosphere model, transfers between the compartments are indicated by arrows

FIGURE F2 Pasture and arable soil model (arable soil single compartment linking to deep soil and caesium recycling optional pasture model extension), transfers between the compartments are indicated by arrows

River

Deep

Arable Pasture

Lake

Deep

Local

compartment

Top

Middle

Deep

Top

Middle

Deep

Regional

marine

Sediment

Deep

Arable ArablePasture Pasture

Soil 2 (1 cm)

Soil 3 (4 cm)

Soil 4 (10 cm)

Soil 5

Soil 6 Deep soil (33 cm)

Soil 1 (30 cm)

Soil 2a

Soil 3a

River Water

Caesium

(15 cm)


58

FIGURE F3 Green vegetable model, transfers between the compartments are indicated by arrows

FIGURE F4 Pasture model including additional compartments for caesium, transfers between the compartments are indicated by arrows

Irrigation

(river/marine)

Soil 0 – 1 cm

Soil 1 – 5 cm

Soil 5 – 15 cm

Soil 15 – 30 cm

Deep soil

External plant 1

External plant 2

Internal plant 1

Internal plant 2

Internal plant 3

FixedExternal plant 1a

External plant 2a

Caesium

Irrigation

(river/marine)

Soil 1 External plant 1

External plant

Internal plant 2

Internal plant 1

Root uptake

Soil

contamination

Cropping

Cropping

Translocation

Translocation

Weathering

APPENDIX F

59

TABLE F4 Comparison of individual doses calculated by BIOS_4A and BIOS_6B for a continuous release of 1 MBq y

–1

Exposure pathway

Dose (Sv y–1

)

99Tc (release period 10

4 years)

235U* (release period 10

5 years)

BIOS_4A BIOS_6B BIOS_4A BIOS_6B

Ingestion

Drinking water 5.8 10–13

5.8 10–13

3.6 10–11

4.4 10–11

Freshwater fish 2.9 10–13

2.9 10–13

1.2 10–11

1.5 10–11

Beef 8.3 10–14

7.8 10–14

3.3 10–11

1.1 10–10

Cow liver 7.4 10–14

6.9 10–14

2.8 10–11

9.8 10–11

Milk 5.6 10–13

5.3 10–13

2.7 10–12

6.5 10–12

Mutton 7.0 10–14

6.5 10–14

2.6 10–11

9.1 10–11

Sheep liver 8.3 10–14

7.8 10–14

1.1 10–10

4.0 10–10

Chicken 6.0 10–14

5.3 10–14

3.9 10–12

8.1 10–12

Eggs 5.0 10–14

4.4 10–14

3.9 10–12

8.6 10–12

Green vegetables 4.4 10–12

4.2 10–12

2.6 10–10

9.5 10–10

Grain 9.9 10–12

9.3 10–12

5.8 10–10

2.1 10–9

Root vegetables 1.2 10–11

1.1 10–11

7.0 10–10

2.5 10–9

Inhalation of resuspended material

Farmer ploughing 1.9 10–16

2.0 10–16

2.4 10–10

4.8 10–10

Arable 1.1 10–15

1.2 10–15

1.4 10–9

2.8 10–9

Pasture 3.3 10–18

3.0 10–18

8.1 10–10

1.6 10–9

External exposure

On arable soil 0.0 – 2.6 10–10

1.4 10–9

On pasture 0.0 – 9.0 10–11

5.5 10–10

* Doses for 235

U include contribution from in-growth of progeny 231

Pa and 227

Ac (see Table A1).

F3 References

Cabianca T, Penfold JSS, Mobbs SF, Barraclough IM, Harvey MP, Oatway WB, Smith KR and Kowe R (to be

published). Assessment of the Radiological Impact of the Landfill Disposal of Small Quantities of Solid

Radioactive Waste by ‘Small Users’.

Ferry C (1996). Le Code GEOS – Version 2 – Calcul des Transferts dans la Géosphère. Théorie et Utilisation.

IPSN/SERGD Technical Report 96/19. Fontenay aux Roses, Institute de Protection et de Sûreté Nucléare.

Hill MD (Editor) (1989). The Verification and Validation of Models for Calculating Rates of Radionuclide Transfer

through the Environment. Chilton, NRPB-R223.

ICRP (2001). ICRP Database of Dose Coefficients: Worker and Members of the Public, Version 2.0.1.

Martin JS, Barraclough IM, Mobbs SF, Klos RA and Lawson G (1991). User Guide for BIOS 3A. Chilton, NRPB-M285.

Smith JG and Simmonds JR (2009). Methodology for Assessing the Radiological Consequences of Routine Releases

of Radionuclides to the Environment Used in PC-CREAM 08. Chilton, HPA-RPD-058.

Smith KR and Jones AL (2003). Generalised Habit Data for Radiological Assessments. Chilton, NRPB-W41.

phe landfill modelling system - gov uk · 7.1 verification of the lms 18 7.1.1 results of the...

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